This paper studies tax withholding on business sales, a widely used compliance mechanism which is largely ignored by public finance theory. The study introduces a withholding scheme, whereby the payer in a transaction collects tax from the payee, in a standard evasion model. If the taxpayer can fully reclaim the tax withheld, withholding is irrelevant to her evasion decision. If reclaim is costly, however, withholding establishes a compliance default. To show this empirically, the analysis exploits a tenyear panel of registration, income tax and sales tax records from 400,000 firms in Costa Rica, and over 20 million thirdparty information and withholding reports. The paper first
Public Disclosure Authorized Public Disclosure Authorized Policy Research Working Paper 7600 Taxation, Information, and Withholding Evidence from Costa Rica Anne Brockmeyer Marco Hernandez Public Disclosure Authorized Public Disclosure Authorized WPS7600 Macroeconomics and Fiscal Management Global Practice Group March 2016 Policy Research Working Paper 7600 Abstract This paper studies tax withholding on business sales, a widely used compliance mechanism which is largely ignored by public finance theory The study introduces a withholding scheme, whereby the payer in a transaction collects tax from the payee, in a standard evasion model If the taxpayer can fully reclaim the tax withheld, withholding is irrelevant to her evasion decision If reclaim is costly, however, withholding establishes a compliance default To show this empirically, the analysis exploits a ten-year panel of registration, income tax and sales tax records from 400,000 firms in Costa Rica, and over 20 million thirdparty information and withholding reports The paper first documents the anatomy of compliance, providing novel measures of compliance gaps on the extensive, intensive and payment margins It then shows that interventions leveraging the existing third-party information reduce these compliance gaps only marginally Coverage by a withholding scheme, in contrast, is correlated with higher reported taxable income both across firms and within firms across time Quasi-experimental estimations show that a doubling of the withholding rate leads to a 40 percent increase in tax payment among treated firms and a 10 percent increase in aggregate revenue The mechanisms are incomplete reclaim of the tax withheld and reduced misreporting This paper is a product of the Macroeconomics and Fiscal Management Global Practice Group It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org The authors may be contacted at abrockmeyer@worldbank.org The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished The papers carry the names of the authors and should be cited accordingly The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors They not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent Produced by the Research Support Team ❚❛①❛t✐♦♥✱ ■♥❢♦r♠❛t✐♦♥✱ ❛♥❞ ❲✐t❤❤♦❧❞✐♥❣✿ ✯ ❊✈✐❞❡♥❝❡ ❢r♦♠ ❈♦st❛ ❘✐❝❛ ❆♥♥❡ ❇r♦❝❦♠❡②❡r✱ ▼❛r❝♦ ❍❡r♥❛♥❞❡③ ✯ ❈♦rr❡s♣♦♥❞✐♥❣ ❛✉t❤♦r✿ ❆♥♥❡ ❇r♦❝❦♠❡②❡r✱ ❛❜r♦❝❦♠❡②❡r❅✇♦r❧❞❜❛♥❦✳♦r❣✳ ▼❛r❝♦ ❍❡r♥❛♥❞❡③✿ ♠❛r❝♦✲ ❤❡r♥❛♥❞❡③❅✇♦r❧❞❜❛♥❦✳♦r❣✳ ❚❤✐s ♣❛♣❡r ✐s st✐❧❧ ❜❡✐♥❣ ✉♣❞❛t❡❞✳ ❚❤❡ ❧❛st ✈❡rs✐♦♥ ❝❛♥ ❜❡ ❢♦✉♥❞ ❛t ❤tt♣s✿✴✴s✐t❡s✳❣♦♦❣❧❡✳❝♦♠✴s✐t❡✴❛♥♥❡❜r♦❝❦♠❡②❡r✇♦r❧❞❜❛♥❦✴❤♦♠❡✳ ❲❡ ❛r❡ ❡①❝❡❡❞✐♥❣❧② ❣r❛t❡❢✉❧ t♦ t❤❡ ▼✐♥✐str② ♦❢ ❋✐✲ ♥❛♥❝❡ ❛♥❞ t❤❡ ●❡♥❡r❛❧ ❉✐r❡❝t♦r② ❢♦r ❚❛①❛t✐♦♥ ♦❢ ❈♦st❛ ❘✐❝❛ ❢♦r ♦✉tst❛♥❞✐♥❣ ❝♦❧❧❛❜♦r❛t✐♦♥✳ ■♥ ♣❛rt✐❝✉❧❛r✱ ✇❡ ❛r❡ ✐♥❞❡❜t❡❞ t♦ ❋❡r♥❛♥❞♦ ❘♦❞r✐❣✉❡③ ●❛rr♦ ❛♥❞ ❈❛r❧♦s ❱❛r❣❛s ❉✉r❛♥✱ ❛s ✇❡❧❧ ❛s t♦ ▲❛✉r❛ ❇❛❞✐❧❧❛ ❈❛str♦✱ ▲♦r❡♥❛ ❈❤❛❝♦♥ ❙❛♥❝❤❡③✱ ●r❛❝✐❡❧❛ ●❛r❝✐❛ ❙❛♥t❛♠❛r✐❛✱ ▼❡r❝❡❞❡s P❛❞✐❧❧❛ ❉❡❧❣❛❞♦✱ ▼❛♥✉❡❧ ❊♥r✐q✉❡ ❘❛♠♦s ❈❛♠♣♦s✱ ❘♦♥❛❧❞ ❙♦❧♦r③❛♥♦ ❱❡❣❛ ❛♥❞ ●✐♦✈❛♥♥✐ ❚❡♥❝✐♦ P❡r❡✐r❛✳ ❲❡ t❤❛♥❦ ❋r❛♥ç♦✐s ●ér❛r❞✱ ❍❡♥r✐❦ ❑❧❡✈❡♥ ❛♥❞ ❏♦❛♥❛ ◆❛r✐t♦♠✐ ❛♥❞ s❡♠✐♥❛r ♣❛r✲ t✐❝✐♣❛♥ts ❛t t❤❡ ◆❛t✐♦♥❛❧ ❚❛① ❆ss♦❝✐❛t✐♦♥ ❝♦♥❢❡r❡♥❝❡✱ P✉❜❧✐❝ ❊❝♦♥♦♠✐❝s ✐♥ t❤❡ ❯❑ ❝♦♥❢❡r❡♥❝❡✱ ❛♥❞ t❤❡ ❲♦r❧❞ ❇❛♥❦ ❢♦r ❤❡❧♣❢✉❧ ❝♦♠♠❡♥ts✳ ❏✉❧✐❛♥❛ ▲♦♥❞♦ñ♦ ❱é❧❡③✱ ❙♣❡♥❝❡r ❙♠✐t❤ ❛♥❞ ●❛❜r✐❡❧ ❚♦✉r❡❦ ♣r♦✈✐❞❡❞ ❡①❝❡❧❧❡♥t r❡s❡❛r❝❤ ❛ss✐st❛♥❝❡✳ ❆❧❧ ❡rr♦rs ❛r❡ ♦✉r ♦✇♥✳ ✶ ■♥tr♦❞✉❝t✐♦♥ ❉❡✈❡❧♦♣✐♥❣ ❡❝♦♥♦♠✐❡s ❛r❡ ❝❤❛r❛❝t❡r✐③❡❞ ❜② ❧♦✇ t❛①✲t♦✲●❉P r❛t✐♦s✱ ❛♥❞ ❛ ❞✐✛❡r❡♥t ♠✐① ♦❢ t❛① ✐♥str✉✲ ♠❡♥ts t❤❛♥ ❤✐❣❤ ✐♥❝♦♠❡ ❝♦✉♥tr✐❡s ✭❇❡s❧❡② ✫ P❡rss♦♥ ✷✵✶✸✱ ❇❡st ❡t ❛❧✳ ✷✵✶✺✮✳ ❲✐t❤❤♦❧❞✐♥❣ ♦♥ ✜r♠s✬ s❛❧❡s ✐s ❛ t❛① ✐♥str✉♠❡♥t t❤❛t ✐s ❡①t❡♥s✐✈❡❧② ✉s❡❞ ✐♥ ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr✐❡s✱ ❛♥❞ ✐♥ ❧♦✇✲❝♦♠♣❧✐❛♥❝❡ s❡❝✲ t♦rs ✐♥ ❤✐❣❤ ✐♥❝♦♠❡ ❝♦✉♥tr✐❡s ✭❙❛♠❛♥❛♠✉❞ ✷✵✶✸✱ ❙♦♦s ✶✾✾✵✱❖❊❈❉ ✷✵✵✾✮✳✶ ■♥ ❛ ✇✐t❤❤♦❧❞✐♥❣ s❝❤❡♠❡✱ t❤❡ ♣❛②❡r ✐♥ ❛ tr❛♥s❛❝t✐♦♥ ✇✐t❤❤♦❧❞s t❛① ❢r♦♠ t❤❡ ♣❛②❡❡✱ r❡♠✐tt✐♥❣ t❤❡ t❛① t♦ t❤❡ ❣♦✈❡r♥♠❡♥t ❛s ❛♥ ❛❞✈❛♥❝❡ t❛① ♣❛②♠❡♥t ❢♦r t❤❡ ♣❛②❡❡✳✷ ❚❤❡ ♣❛②❡r ❝✉♠ ✇✐t❤❤♦❧❞✐♥❣ ❛❣❡♥t ❝❛♥ ❜❡ ❛ st❛t❡ ❛❣❡♥❝②✱ ✜♥❛♥❝✐❛❧ ✐♥st✐t✉t✐♦♥✱ ♦r ❛♥♦t❤❡r ✜r♠✳ ❚❤❡ ✇✐❞❡s♣r❡❛❞ ✉s❡ ♦❢ ✇✐t❤❤♦❧❞✐♥❣ st❛♥❞s ✐♥ ❝♦♥tr❛st t♦ t❤❡ t❤❡♦r❡t✐❝❛❧ ♣r❡❞✐❝t✐♦♥ t❤❛t ✇✐t❤❤♦❧❞✲ ✐♥❣ s❤♦✉❧❞ ❜❡ ✐rr❡❧❡✈❛♥t t♦ ❡✈❛s✐♦♥✳ ■❢ t❤❡ t❛①♣❛②❡r ❝❛♥ ❝❧❛✐♠ ❢✉❧❧ ❝r❡❞✐t ❢♦r t❛① ✇✐t❤❤❡❧❞✱ ✇✐t❤❤♦❧❞✐♥❣ ✐s ♠❡r❡❧② ❛ ❞✐✛❡r❡♥t ♠❡t❤♦❞ ♦❢ t❛① ❝♦❧❧❡❝t✐♦♥✳ ■t s❤✐❢ts t❤❡ ❝♦❧❧❡❝t✐♦♥ t❛s❦ ❢r♦♠ t❤❡ t❛① ❛✉t❤♦r✐t✐❡s t♦ t❤❡ ✇✐t❤❤♦❧❞✐♥❣ ❛❣❡♥t✱ ✇✐t❤ ♥♦ ❞✐r❡❝t r❡❧❡✈❛♥❝❡ ❢♦r ❡✈❛s✐♦♥ ❞❡❝✐s✐♦♥s✳ ■♥ ❈♦st❛ ❘✐❝❛✱ t❤❡ ❧❛✇ st❛t❡s t❤❛t t❛① ✇✐t❤❤❡❧❞ ✐s ❢✉❧❧② ❝r❡❞✐t❛❜❧❡ ❛❣❛✐♥st ❛ t❛①♣❛②❡r✬s ✐♥❝♦♠❡ ♦r s❛❧❡s t❛① ❧✐❛❜✐❧✐t② ❛♥❞ ❝❛♥ ❣✐✈❡ r✐s❡ t♦ ❛ ❝❛s❤ r❡❢✉♥❞ ✐❢ t❤❡ ❛♠♦✉♥t ✇✐t❤❤❡❧❞ ❡①❝❡❡❞s t❤❡ ❧✐❛❜✐❧✐t②✳ ■♥ ♣r❛❝t✐❝❡✱ ❤♦✇❡✈❡r✱ ✐t ✐s ❝♦st❧② ❢♦r t❤❡ t❛①♣❛②❡r t♦ r❡❝❧❛✐♠ t❤❡ t❛① ✇✐t❤❤❡❧❞✳ ❚❛①♣❛②❡rs ✐♥❝✉r ❛♥ ❛❞♠✐♥✐str❛t✐✈❡ ❝♦st t♦ ♠❛❦❡ ❛ r❡❝❧❛✐♠✱ t❤❡② ❝❛♥ r❡❝❧❛✐♠ ♦♥❧② ✐❢ t❤❡② ❛r❡ ❝♦♠♣❧✐❛♥t ♦♥ t❤❡ ❡①t❡♥s✐✈❡ ♠❛r❣✐♥✱ ❛♥❞ r❡❝❧❛✐♠❡rs ♠❛② ❢❛❝❡ ❛ ❤✐❣❤❡r ❛✉❞✐t ♣r♦❜❛❜✐❧✐t②✳ ❋♦r t❤❡s❡ r❡❛s♦♥s✱ ✇✐t❤❤♦❧❞✐♥❣ ❝❛♥ ❡st❛❜❧✐s❤ ❛ ❝♦♠♣❧✐❛♥❝❡ ❞❡❢❛✉❧t✱ ✐♥❝r❡❛s✐♥❣ t♦t❛❧ t❛① ♣❛②♠❡♥t✳ ❚❤✐s ♣❛♣❡r st✉❞✐❡s t❤❡ ❝♦♠♣❧✐❛♥❝❡ ✐♠♣❛❝t ♦❢ ✇✐t❤❤♦❧❞✐♥❣ ❝♦♥❝❡♣t✉❛❧❧② ❛♥❞ ❡♠♣✐r✐❝❛❧❧②✳ ❲❡ st❛rt ❜② ✐♥tr♦❞✉❝✐♥❣ ✇✐t❤❤♦❧❞✐♥❣ ✐♥ ❛ s✐♠♣❧❡ ♠♦❞❡❧ ♦❢ t❛① ❡✈❛s✐♦♥ ❢♦❧❧♦✇✐♥❣ ❆❧❧✐♥❣❤❛♠ ✫ ❙❛♥❞♠♦ ✭✶✾✼✷✮✳ ❲❡ s❤♦✇ t❤❛t✱ ✐❢ t❤❡ ✇✐t❤❤❡❧❞ t❛① ❝❛♥ ❜❡ ❢✉❧❧② r❡❝❧❛✐♠❡❞✱ ✇✐t❤❤♦❧❞✐♥❣ ✐s ✐rr❡❧❡✈❛♥t t♦ t❤❡ t❛①♣❛②❡r✬s ❡✈❛s✐♦♥ ❞❡❝✐s✐♦♥✳ ❲❡ t❤❡♥ ♣r♦♣♦s❡ ❛ ♠♦❞❡❧ ✇✐t❤ ❝♦st❧② r❡❝❧❛✐♠✱ ✇❤✐❝❤ ♣r❡❞✐❝ts t❤❛t ♦♥❧② ❛ ❢r❛❝t✐♦♥ ♦❢ t❛①♣❛②❡rs r❡❝❧❛✐♠ t❤❡ t❛① ✇✐t❤❤❡❧❞ ❛♥❞ ❛♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ✐♥❝r❡❛s❡s r❡♣♦rt❡❞ t❛①❛❜❧❡ ✐♥❝♦♠❡✳ ❚♦ t❡st t❤❡ ♣r❡❞✐❝t✐♦♥s ♦❢ ♦✉r ♠♦❞❡❧ ❡♠♣✐r✐❝❛❧❧②✱ ✇❡ ❡①♣❧♦✐t ✈❛r✐♦✉s s♦✉r❝❡s ♦❢ q✉❛s✐✲❡①♣❡r✐♠❡♥t❛❧ ✈❛r✐❛t✐♦♥ ✐♥ t❤❡ ✐♥❝♦♠❡ ❛♥❞ s❛❧❡s t❛① s②st❡♠ ✐♥ ❈♦st❛ ❘✐❝❛✱ ❛♥❞ ❛ ♥✐♥❡✲②❡❛r ♣❛♥❡❧ ♦❢ ❛❞♠✐♥✐str❛✲ t✐✈❡ t❛① r❡❝♦r❞s✳ ❲❡ ❝♦♥str✉❝t t❤❡ ❈♦st❛ ❘✐❝❛♥ t❛① r❡❣✐st❡r ❢r♦♠ t❤❡ ✉♥✐✈❡rs❡ ♦❢ r❡❣✐str❛t✐♦♥ ❛♥❞ ❞❡r❡❣✐str❛t✐♦♥ r❡❝♦r❞s s✐♥❝❡ ✷✵✵✻✳ ❲❡ ♠❛t❝❤ t❤❡ r❡❣✐st❡r ✇✐t❤ ✐♥❝♦♠❡ ❛♥❞ s❛❧❡s t❛① r❡❝♦r❞s ❢r♦♠ t❤❡ ✉♥✐✈❡rs❡ ♦❢ ✜r♠s✱ ✐♥❝❧✉❞✐♥❣ ❜♦t❤ s❡❧❢✲❡♠♣❧♦②❡❞ ❛♥❞ ❝♦r♣♦r❛t✐♦♥s✳ ❲❡ ❢✉rt❤❡r ♠❛t❝❤ t❤❡s❡ ❞❛t❛ ✶ ❚❤✐s ✐s ❞✐st✐♥❝t ❢r♦♠ ✇✐t❤❤♦❧❞✐♥❣ ♦♥ ✇❛❣❡s✱ ❛ t❛① ❝♦♠♣❧✐❛♥❝❡ ♠❡❝❤❛♥✐s♠ t❤❛t ✐s ❛♣♣❧✐❡❞ ❛❧♠♦st ✉♥✐✈❡rs❛❧❧② ❛♥❞ ✇❡❧❧ ✉♥❞❡rst♦♦❞ ✭❑❧❡✈❡♥ ❡t ❛❧✳ ✷✵✶✶✮✳ ❙❡❡ ❋✐❣✉r❡ ■ ❢♦r ❛ ♣r❡❧✐♠✐♥❛r② ❛♥❛❧②s✐s ♦❢ t❤❡ ✉s❡ ♦❢ s❛❧❡s ✇✐t❤❤♦❧❞✐♥❣ ❜② ❝♦✉♥tr② ✐♥❝♦♠❡ ❧❡✈❡❧s✳ ✷ ■♥ s♦♠❡ ❝♦✉♥tr✐❡s✱ t❤❡ ♣❛②❡❡ ❛❧s♦ ✇✐t❤❤♦❧❞s ❢r♦♠ t❤❡ ♣❛②❡r✱ ❛❞❞✐♥❣ t❛① t♦ t❤❡ ✐♥✈♦✐❝❡✳ ✷ ✇✐t❤ ♦✈❡r ✷✵ ♠✐❧❧✐♦♥ t❤✐r❞✲♣❛rt② ❛♥❞ ✇✐t❤❤♦❧❞✐♥❣ r❡❝♦r❞s ❢r♦♠ ✜r♠s✬ tr❛♥s❛❝t✐♦♥ ♣❛rt♥❡rs✱ ✜♥❛♥❝✐❛❧ ✐♥st✐t✉t✐♦♥s ❛♥❞ st❛t❡ ✐♥st✐t✉t✐♦♥s✳ ❲❡ ♠❛t❝❤ ❡❛❝❤ ✜r♠ ✇✐t❤ t❤❡ ✐♥❢♦r♠❛t✐♦♥ r❡♣♦rts ✐t ♣r♦✈✐❞❡❞ ❛♥❞ t❤❡ ✐♥❢♦r♠❛t✐♦♥ r❡♣♦rts r❡❝❡✐✈❡❞ ❛❜♦✉t ✐ts ❛❝t✐✈✐t✐❡s✳ ❖✉r ❛♥❛❧②s✐s ✐s ❞✐✈✐❞❡❞ ✐♥t♦ t✇♦ ♣❛rts✳ ■♥ t❤❡ ✜rst ♣❛rt✱ ✇❡ ❧❡✈❡r❛❣❡ t❤❡ ❞❛t❛ t♦ ❝♦♥❞✉❝t ❛ ❞❡t❛✐❧❧❡❞ ❛♥❛t♦♠② ♦❢ ❝♦♠♣❧✐❛♥❝❡✳✸ ❚♦ ♦✉r ❦♥♦✇❧❡❞❣❡✱ t❤✐s ✐s t❤❡ ✜rst st✉❞② t♦ ✉s❡ ♣♦♣✉❧❛t✐♦♥✲✇✐❞❡ t❤✐r❞✲♣❛rt② ❛♥❞ ✇✐t❤❤♦❧❞✐♥❣ ❞❛t❛ ❢r♦♠ ❛ ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr②✱ ❛♥❞ t♦ ❛♥❛❧②③❡ ❛❧❧ ❝♦♠♣❧✐❛♥❝❡ ♠❛r❣✐♥s✱ ✐♥❝❧✉❞✐♥❣ t❤❡ ❡①t❡♥s✐✈❡✱ ✐♥t❡♥s✐✈❡ ❛♥❞ ♣❛②♠❡♥t ♠❛r❣✐♥✳ ❖♥ t❤❡ ❡①t❡♥s✐✈❡ ♠❛r❣✐♥✱ ✇❡ ✜♥❞ t❤❛t ♦✈❡r ✸✵✪ ♦❢ t❛①✲❧✐❛❜❧❡ ✜r♠s ❢❛✐❧ t♦ ✜❧❡ ❛ s❡❧❢✲❛ss❡ss♠❡♥t ❞❡❝❧❛r❛t✐♦♥ ❢♦r t❤❡ ✐♥❝♦♠❡ t❛①✳ ❚❤❡ s❤❛r❡ ♦❢ ♥♦♥✲✜❧❡rs ✐s ❡q✉❛❧❧② ❤✐❣❤ ✐♥ t❤❡ s✉❜s❛♠♣❧❡ ♦❢ t❛①✲ ❧✐❛❜❧❡ ✜r♠s ❝♦✈❡r❡❞ ❜② t❤✐r❞✲♣❛rt② ✐♥❢♦r♠❛t✐♦♥ ❛♥❞ t❤✉s ❞❡✜♥✐t❡❧② ✐❞❡♥t✐✜❡❞ ❛s ❡❝♦♥♦♠✐❝❛❧❧② ❛❝t✐✈❡✳ ❖✈❡r❛❧❧✱ ✶✵✪ ♦❢ t❤✐r❞✲♣❛rt② r❡♣♦rt❡❞ s❛❧❡s ❛r❡ ♥♦t ❞❡❝❧❛r❡❞ ❜② t❤❡ t❛①♣❛②❡r✳ ❯♥❧✐❦❡ s✉r✈❡② ♦r ♠❛❝r♦✲ ❜❛s❡❞ ♠❡❛s✉r❡s ♦❢ ✐♥❢♦r♠❛❧✐t②✱ ♦✉r ♠❡t❤♦❞ ✉s❡s ♠✐❝r♦✲❛❞♠✐♥✐str❛t✐✈❡ ❞❛t❛ t♦ ✐❞❡♥t✐❢② ❝♦♠♣❧✐❛♥❝❡ ❣❛♣s ❛t t❤❡ ♠❛r❣✐♥ ❜❡t✇❡❡♥ ❢✉❧❧ ✐♥❢♦r♠❛❧✐t② ❛♥❞ ❢♦r♠❛❧✐t②✳ ❖✉r ❡st✐♠❛t❡s ❞♦ ♥♦t ❝❛♣t✉r❡ ❢✉❧❧② ✐♥❢♦r♠❛❧ ✜r♠s✱ ❜✉t ✇❡ ❛r❣✉❡ t❤❛t t❤❡② ✐❞❡♥t✐❢② t❤❡ ♣♦❧✐❝② r❡❧❡✈❛♥t s❡❣♠❡♥t ♦❢ t❛① ♣❛②❡rs ✐♥ ✇❤✐❝❤ ❝♦♠♣❧✐❛♥❝❡ ❝❛♥ ❜❡ ❡♥❤❛♥❝❡❞ ❛t ❧♦✇ ❝♦st✳✹ ❲❡ ❛❧s♦ ✜♥❞ s✐❣♥✐✜❝❛♥t ❝♦♠♣❧✐❛♥❝❡ ❣❛♣s ♦♥ t❤❡ ✐♥t❡♥s✐✈❡ ♠❛r❣✐♥✱ ❛s ❡✈✐❞❡♥❝❡❞ ❜② ✉♥❞❡r✲r❡♣♦rt✐♥❣ ♦❢ s❛❧❡s ❝♦♠♣❛r❡❞ t♦ t❤✐r❞✲♣❛rt② ✐♥❢♦r♠❛t✐♦♥✱ ❛♥❞ ❧❛r❣❡ ❛♥❞ s❤❛r♣ ❜✉♥❝❤✐♥❣ ❛t t❤❡ ✜rst ✐♥❝♦♠❡ t❛① ❦✐♥❦✳✺ ❚❤❡ s❤❛r❡ ♦❢ ✉♥❞❡r✲r❡♣♦rt❡rs ❢♦r t❤❡ ✐♥❝♦♠❡ t❛① ❝♦♥st✐t✉t❡s ✶✽✪ ♦❢ t❤❡ s❡❧❢✲❡♠♣❧♦②❡❞ ❛♥❞ ✾✪ ♦❢ ❝♦r♣♦r❛t✐♦♥s✳ ■♥ t❤✐s s❛♠♣❧❡ ♦❢ ✉♥❞❡r✲r❡♣♦rt❡rs✱ ♦✈❡r ✹✵✪ ♦❢ t❤✐r❞✲♣❛rt② r❡♣♦rt❡❞ s❛❧❡s r❡♠❛✐♥ ✉♥❞❡❝❧❛r❡❞✳ ❚❤❡s❡ ❝♦♠♣❧✐❛♥❝❡ ❣❛♣s ♣❡rs✐st ❡✈❡♥ s❡✈❡r❛❧ ②❡❛rs ❛❢t❡r t❤❡ r❡❧❡✈❛♥t ✜❧✐♥❣ ♣❡r✐♦❞✱ ❛♥❞ ❞❡s♣✐t❡ s②st❡♠❛t✐❝ ❣♦✈❡r♥♠❡♥t ❝r♦ss✲❝❤❡❝❦s ♦❢ t❤✐r❞✲♣❛rt② ✐♥❢♦r♠❛t✐♦♥ ✇✐t❤ t❛① r❡❝♦r❞s✳✻ ❖♥ t❤❡ ♣❛②♠❡♥t ♠❛r❣✐♥✱ ✇❡ ✜♥❞ t❤❛t ❝♦♠♣❧✐❛♥❝❡ ✐s r❡❧❛t✐✈❡❧② ❤✐❣❤✱ ❛❧t❤♦✉❣❤ ❛ ♥♦♥✲♥❡❣❧❡❣✐❜❧❡ ❢r❛❝t✐♦♥ ♦❢ s♠❛❧❧ ✜r♠s ♣❛② t❤❡✐r ❧✐❛❜✐❧✐t✐❡s ✇✐t❤ s❡✈❡r❛❧ ②❡❛rs ♦❢ ❞❡❧❛②✳ ❚♦❣❡t❤❡r✱ t❤✐s ❡✈✐❞❡♥❝❡ ♦❢ ♥♦♥✲✜❧✐♥❣✱ ♠✐sr❡♣♦rt✐♥❣ ♦♥ t❤❡ ✐♥t❡♥s✐✈❡ ♠❛r❣✐♥ ❛♥❞ s✐❣♥✐✜❝❛♥t ♣❛②♠❡♥t ❞❡❧❛②s ❛♠♦♥❣ s♠❛❧❧ t❛①♣❛②❡rs s✉❣❣❡sts t❤❛t t❤❡r❡ ❛r❡ ❧✐♠✐ts t♦ t❤❡ ❡①t❡♥t t♦ ✇❤✐❝❤ t❤✐r❞✲♣❛rt② ✐♥❢♦r♠❛t✐♦♥✱ r❡♠✐♥❞❡rs ❛♥❞ ❛✉❞✐ts ❝❛♥ ❤❡❧♣ t♦ ❡♥❤❛♥❝❡ t❛① ❝♦♠♣❧✐❛♥❝❡✳ ❚❤✐s ♣r♦✈✐❞❡s ❛ r❛t✐♦♥❛❧❡ ❢♦r t❤❡ ✉s❡ ♦❢ ✇✐t❤❤♦❧❞✐♥❣ ❛s ❛♥ ❛❧t❡r♥❛t✐✈❡ ❡♥❢♦r❝❡♠❡♥t ♠❡❝❤❛♥✐s♠✳ ✸ ❲❡ ❜♦rr♦✇ t❤❡ t❡r♠ ❢r♦♠ ❑❧❡✈❡♥ ❡t ❛❧✳ ✭✷✵✶✶✮ ✇❤♦ ❝♦♥❞✉❝t ❛♥ ❛♥❛t♦♠② ♦❢ ❝♦♠♣❧✐❛♥❝❡ ❢♦r ✇❛❣❡ ❡❛r♥❡rs ❛♥❞ t❤❡ s❡❧❢✲❡♠♣❧♦②❡❞ ✐♥ ❉❡♥♠❛r❦✳ ✹ ■♥ ❛ ❝♦♠♣❛♥✐♦♥ ♣❛♣❡r✱ ❇r♦❝❦♠❡②❡r ❡t ❛❧✳ ✭✷✵✶✺✮ s❤♦✇ t❤❛t ❝r❡❞✐❜❧❡ ❞❡t❡rr❡♥❝❡ ♠❡ss❛❣❡s ❢r♦♠ t❤❡ t❛① ❛✉t❤♦r✐t✐❡s s✐❣♥✐✜❝❛♥t❧② ✐♥❝r❡❛s❡ t❛① ✜❧✐♥❣ ❛♥❞ ♣❛②♠❡♥t ❛♠♦♥❣ t❤❡s❡ ✜r♠s✳ ✺ Pr❡✈✐♦✉s st✉❞✐❡s ❤❛✈❡ s❤♦✇♥ t❤❛t ❜✉♥❝❤✐♥❣ ✐s ❧❛r❣❡❧② ❞r✐✈❡♥ ❜② ♠✐sr❡♣♦rt✐♥❣ r❛t❤❡r t❤❛♥ r❡❛❧ r❡s♣♦♥s❡s ✭❡✳❣✳ ❇❡st ❡t ❛❧✳ ✷✵✶✺ ❢♦r t❤❡ ♠✐♥✐♥✉♠ t❛① ❦✐♥❦ ✐♥ P❛❦✐st❛♥✱ ❆❧♠✉♥✐❛ ✫ ❘♦❞r✐❣✉❡③ ✷✵✶✺ ❢♦r ❛♥ ❡♥❢♦r❝❡♠❡♥t ♥♦t❝❤ ✐♥ t❤❡ ❙♣❛♥✐s❤ ❝♦r♣♦r❛t✐♦♥ t❛①✮✳ ✻ ❚❤❡s❡ ❡st✐♠❛t❡s ❛r❡ ❧♦✇❡r t❤❛♥ s✐♠✐❧❛r ❡st✐♠❛t❡s ❢♦r ✜r♠s ✐♥ ❊❝✉❛❞♦r ❢r♦♠ ❈❛rr✐❧❧♦ ❡t ❛❧✳ ✭✷✵✶✹✮✳ ❍♦✇❡✈❡r✱ ❣✐✈❡♥ t❤❡ ✐♥❝♦♠♣❧❡t❡♥❡ss ♦❢ t❤✐r❞✲♣❛rt② r❡❝♦r❞s✱ ♦✉r ❡st✐♠❛t❡s ❛r❡ ✇❡❛❦ ❧♦✇❡r ❜♦✉♥❞s ♦♥ ❡✈❛s✐♦♥✱ ❛♥❞ ✇❡❛❦❡r ❝♦♠♣❛r❡❞ t♦ ❈❛rr✐❧❧♦ ❡t ❛❧✳ ✭✷✵✶✹✮ ✇❤♦ ❛❧s♦ ✉s❡❞ ❝✉st♦♠s ❞❛t❛✳ ✸ ❲❡ t✉r♥ t♦ ❛♥❛❧②③❡ t❤❡ ✐♠♣❛❝t ♦❢ ✇✐t❤❤♦❧❞✐♥❣ ✐♥ t❤❡ s❡❝♦♥❞ ♣❛rt✳ ❲❡ ❜❡❣✐♥ ❜② s❤♦✇✐♥❣ t❤❛t ❝♦✈❡r❛❣❡ ❜② ❛ ✇✐t❤❤♦❧❞✐♥❣ s❝❤❡♠❡ ✐s str♦♥❣❧② ❝♦rr❡❧❛t❡❞ ✇✐t❤ ❤✐❣❤❡r r❡♣♦rt❡❞ t❛①❛❜❧❡ ✐♥❝♦♠❡ ❛❝r♦ss ✜r♠s ❛♥❞ ✇✐t❤✐♥ ✜r♠s ❛❝r♦ss t✐♠❡✳ ❆❝r♦ss ✜r♠s✱ ✇❡ ✜♥❞ t❤❛t ❜✉♥❝❤✐♥❣ ✐s s✐❣♥✐✜❝❛♥t❧② s♠❛❧❧❡r ❛♠♦♥❣ ✜r♠s ❝♦✈❡r❡❞ ❜② t❤✐r❞✲♣❛rt② ✐♥❢♦r♠❛t✐♦♥ r❡♣♦rt✐♥❣ ❛♥❞ ❡✈❡♥ s♠❛❧❧❡r ❛♠♦♥❣ ✜r♠s s✉❜❥❡❝t t♦ ✇✐t❤❤♦❧❞✐♥❣✱ ❡✐t❤❡r ❜② ❛ st❛t❡ ✐♥st✐t✉t✐♦♥ ♦r ❜② t❤❡✐r ❝r❡❞✐t✴❞❡❜✐t ❝❛r❞ ♣r♦✈✐❞❡r✳ ❆❝r♦ss t✐♠❡✱ ✇❡ ✜♥❞ t❤❛t ✜r♠s t❤❛t ❜❡❝♦♠❡ s✉❜❥❡❝t t♦ ✇✐t❤❤♦❧❞✐♥❣ ❡①❤✐❜✐t ❛ s✐❣♥✐✜❝❛♥t ✐♥❝r❡❛s❡ ✐♥ r❡♣♦rt❡❞ t❛①❛❜❧❡ ✐♥❝♦♠❡ ♣r❡❝✐s❡❧② ✐♥ t❤❡ ②❡❛r ✐♥ ✇❤✐❝❤ t❤❡② ❛r❡ s✉❜❥❡❝t t♦ ✇✐t❤❤♦❧❞✐♥❣ ❢♦r t❤❡ ✜rst t✐♠❡✳ ❲❡ t❤❡♥ ❡①♣❧♦✐t ❛ s❛❧❡s t❛① ✇✐t❤❤♦❧❞✐♥❣ r❡❢♦r♠ ✐♥ ❛ ❞✐✛❡r❡♥❝❡✲✐♥✲❞✐✛❡r❡♥❝❡ ❞❡s✐❣♥✱ ✜♥❞✐♥❣ t❤❛t ❛ ❞♦✉❜❧✐♥❣ ♦❢ t❤❡ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ❧❡❛❞s t♦ ❛♥ ❛♣♣r♦①✐♠❛t❡❧② ✹✵✪ ✐♥❝r❡❛s❡ ✐♥ t♦t❛❧ t❛① ♣❛②♠❡♥t ❛♠♦♥❣ t❛①♣❛②❡rs s✉❜❥❡❝t t♦ ✇✐t❤❤♦❧❞✐♥❣✳ ■♥ ❛❣❣r❡❣❛t❡✱ t❤❡ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ r❡❢♦r♠ ✐♥❝r❡❛s❡❞ s❛❧❡s t❛① ♣❛②♠❡♥ts ❜② ❛❜♦✉t ✶✵✪✳✼ ❚❤✐s r❡s♣♦♥s❡ ✐s ❞r✐✈❡♥ ❜② ✐♥❝♦♠♣❧❡t❡ r❡❝❧❛✐♠ ♦❢ t❤❡ t❛① ✇✐t❤❤❡❧❞✱ ❛♥❞ ❛♥ ✐♥❝r❡❛s❡ ✐♥ r❡♣♦rt❡❞ t❛①❛❜❧❡ ✐♥❝♦♠❡ ❛♠♦♥❣ ✜r♠s s✉❜❥❡❝t t♦ ✇✐t❤❤♦❧❞✐♥❣✳ ❚❤✐s ❝♦♥✜r♠s t❤❡ ✐♠♣❛❝t ♠❡❝❤❛♥✐s♠s ♣r❡❞✐❝t❡❞ ❜② ♦✉r ❝♦♥❝❡♣t✉❛❧ ❢r❛♠❡✇♦r❦✳ ❲❡ ❛❧s♦ ❝♦♥✜r♠ t❤❛t ♦♥❧② ❛ t✐♥② ❢r❛❝t✐♦♥ ♦❢ t❛①♣❛②❡rs r❡❝❧❛✐♠ t❤r♦✉❣❤ ♦t❤❡r ❝❤❛♥♥❡❧s✱ ❢♦r ✐♥st❛♥❝❡ ♦♥ ❛♥♦t❤❡r t❛① ❞❡❝❧❛r❛t✐♦♥ ♦r ❜② r❡q✉❡st✐♥❣ ❛ ❝❛s❤ r❡❢✉♥❞✳✽ ❲❡ ❝♦♥❝❧✉❞❡ t❤❛t ✇✐t❤❤♦❧❞✐♥❣ ✐♥❝r❡❛s❡s t❛① ♣❛②♠❡♥ts ❜② ❡st❛❜❧✐s❤✐♥❣ ❛ ❝♦♠♣❧✐❛♥❝❡ ❞❡❢❛✉❧t✳ ❖✉r ♣❛♣❡r ❝♦♥tr✐❜✉t❡s t♦ s❡✈❡r❛❧ str❛♥❞s ♦❢ ❧✐t❡r❛t✉r❡✳ ❋✐rst✱ ♦✉r ✇♦r❦ ❝♦♥tr✐❜✉t❡s t♦ t❤❡ ❧✐t❡r❛t✉r❡ ♦♥ t❛①❛t✐♦♥ ❛♥❞ ❞❡✈❡❧♦♣♠❡♥t✱ ❛s r❡✈✐❡✇❡❞ ✐♥ ❇❡s❧❡② ✫ P❡rss♦♥ ✷✵✶✸✳ ❚❤❡♦r❡t✐❝❛❧ ❝♦♥tr✐❜✉t✐♦♥s ✐♥ t❤✐s ❧✐t❡r❛t✉r❡ ❤❛✈❡ ❞✐s❝✉ss❡❞ ✇❤② t❛① s②st❡♠s ✐♥ ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr✐❡s ❞✐✛❡r ❢r♦♠ t❤♦s❡ ✐♥ ❤✐❣❤ ✐♥❝♦♠❡ ❝♦✉♥tr✐❡s ✭❑❡❡♥ ✷✵✵✽✱ ●♦r❞♦♥ ✫ ▲✐ ✷✵✵✾✱ ❇❡st ❡t ❛❧✳ ✷✵✶✺✮✳ ❖✉r r❡s✉❧ts ❡①♣❧❛✐♥ t❤❡ ♣r❡✈❛❧❡♥❝❡ ♦❢ ✇✐t❤❤♦❧❞✐♥❣ s❝❤❡♠❡s ❢♦r ✜r♠s ❛s ❛♥ ❡♥❢♦r❝❡♠❡♥t t♦♦❧ ✐♥ ❧♦✇✲❝♦♠♣❧✐❛♥❝❡ ❡♥✈✐r♦♥♠❡♥ts✳ ❚❤❡② ❛❧s♦ ❤✐❣❤❧✐❣❤t t❤❡ ✐♠♣♦rt❛♥t r♦❧❡ ♦❢ ✜r♠s ✐♥ ❡♥❢♦r❝✐♥❣ t❛①❡s ✭❤❡r❡ ❛s ✇✐t❤❤♦❧❞✐♥❣ ❛❣❡♥ts✮✱ ❛s s✉❣❣❡st❡❞ t❤❡♦r❡t✐❝❛❧❧② ❜② ❑♦♣❝③✉❦ ✫ ❙❧❡♠r♦❞ ✭✷✵✵✻✮ ❛♥❞ ❑❧❡✈❡♥ ❡t ❛❧✳ ✭✷✵✶✺✮✱ ❛♥❞ ❞❡♠♦♥str❛t❡❞ ❡♠♣✐r✐❝❛❧❧② ❜② ❇❡st ✭✷✵✶✹✮ ✐♥ t❤❡ ❝♦♥t❡①t ♦❢ ❡♠♣❧♦②❡r r❡♣♦rt✐♥❣ ♦♥ ❡♠♣❧♦②❡❡s✬ ❡❛r♥✐♥❣s✳ ■♥ ❛❞❞✐t✐♦♥✱ ♦✉r r❡s✉❧ts ❝♦♥tr✐❜✉t❡ t♦ t❤❡ ❡♠♣✐r✐❝❛❧ ❧✐t❡r❛t✉r❡ ♦♥ t❤✐r❞✲♣❛rt② r❡♣♦rt✐♥❣ ❛♥❞ ❝♦♠♣❧✐❛♥❝❡ ✭❈❛rr✐❧❧♦ ❙❧❡♠r♦❞ ❡t ❛❧✳ ✷✵✶✹✱ ❡t ❛❧✳ ✷✵✶✺✱ P♦♠❡r❛♥③ ✷✵✶✺✱ ◆❛r✐t♦♠✐ ✷✵✶✺✮✳ ❈♦♥s✐st❡♥t ✇✐t❤ ❈❛rr✐❧❧♦ ❡t ❛❧✳ ✭✷✵✶✹✮✱ ✇❡ ✜♥❞ ✉♥❞❡r✲r❡♣♦rt✐♥❣ ♦❢ s❛❧❡s ❛s ✇❡❧❧ ❛s ❝♦sts✳ ❲❡ ❛❧s♦ ✜♥❞ t❤❛t t❤❡ ♣r❡s❡♥❝❡ ♦❢ t❤✐r❞✲♣❛rt② ✐♥❢♦r♠❛t✐♦♥ ✐s ❝♦rr❡❧❛t❡❞ ✇✐t❤ ❝♦♠♣❧✐❛♥❝❡ ♦♥ t❤❡ ✐♥t❡♥s✐✈❡ ♠❛r❣✐♥✱ ❛♥❞ ♦♥ t❤❡ ❡①t❡♥s✐✈❡ ♠❛r❣✐♥ ❛♠♦♥❣ r❡❣✐st❡r❡❞ ✜r♠s✳ ❋✐♥❛❧❧②✱ ♦✉r ♣❛♣❡r ♣r♦✈✐❞❡s ♥♦✈❡❧ ❡st✐♠❛t❡s ♦❢ ❡①t❡♥s✐✈❡ ♠❛r❣✐♥ ❝♦♠♣❧✐❛♥❝❡ ❣❛♣s ❛♥❞ ♣❛②♠❡♥t ❝♦♠♣❧✐❛♥❝❡✳ ❙❤❡❞❞✐♥❣ ❧✐❣❤t ♦♥ s✉❜st❛♥t✐❛❧ ♣❛②♠❡♥t ❞❡❧❛②s✱ ✇❡ ❤✐❣❤❧✐❣❤t t❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ ❛♥❛❧②③✐♥❣ ♣❛②♠❡♥t ❞❛t❛ ✐♥ ❛❞❞✐t✐♦♥ t♦ t❛① ❧✐❛❜✐❧✐t② ❞❛t❛✱ ✇❤✐❝❤ ♣r❡✈✐♦✉s st✉❞✐❡s ❤❛✈❡ ❢♦❝✉s❡❞ ♦♥✳ ✼ ✽ ❖✈❡r❛❧❧✱ ✇✐t❤❤♦❧❞✐♥❣ ❛❣❡♥ts ❝♦❧❧❡❝t❡❞ ✶✵✪ ♦❢ ❝♦r♣♦r❛t❡ ✐♥❝♦♠❡ t❛① r❡✈❡♥✉❡ ❛♥❞ ✷✵✪ ♦❢ s❛❧❡s t❛① r❡✈❡♥✉❡ ✐♥ ✷✵✶✹✳ ❘❡s✉❧ts ❛✈❛✐❧❛❜❧❡ ✉♣♦♥ r❡q✉❡st✳ ✹ ❙❡❝♦♥❞✱ ♦✉r st✉❞② ❡①t❡♥❞s t❤❡ ❧✐t❡r❛t✉r❡s ♦♥ t❛① ✇✐t❤❤♦❧❞✐♥❣ ❛♥❞ t❤❡ ✐♠♣❛❝t ♦❢ ❞❡❢❛✉❧ts✳ ❆ ❧❛r❣❡ ❧✐t❡r❛t✉r❡ ❤❛s ❛♥❛❧②③❡❞ ✇✐t❤❤♦❧❞✐♥❣ ❢♦r t❤❡ ♣❡rs♦♥❛❧ ✐♥❝♦♠❡ t❛①✱ ❢♦❝✉s✐♥❣ ♠♦st❧② ♦♥ t❤❡ ❯♥✐t❡❞ ❙t❛t❡s ✭❇❛rr ✫ ❉♦❦❦♦ ✷✵✵✽✱ ●❛♥❞❤✐ ✫ ❑✉❡❤❧✇❡✐♥ ✷✵✶✹✱ ❲❤✐t❡ ❡t ❛❧✳ ✶✾✾✸✱ ❍✐❣❤✜❧❧ ❡t ❛❧✳ ✶✾✾✽✮✳ ❆s✐❞❡ ❢r♦♠ ❞❡s❝r✐♣t✐✈❡ ♣♦❧✐❝② r❡♣♦rts ✭❙❛♠❛♥❛♠✉❞ ✷✵✶✸✱ ❖❊❈❉ ✷✵✵✾✮ ❛♥❞ ❧❡❣❛❧ ✇r✐t✐♥❣ ✭❙♦♦s ✶✾✾✵✮✱ t❤❡ ♦♥❧② st✉❞② ❛♥❛❧②③✐♥❣ ✇✐t❤❤♦❧❞✐♥❣ ♦♥ ✜r♠s ✐s ❈❛r✐❧❧♦ ❡t ❛❧✳ ✭✷✵✶✷✮✳ ❚❤❡② s❤♦✇ t❤❛t ✜r♠s ❜✉♥❝❤ ❛t ❛ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ❦✐♥❦✱ ❛♥❞ ✐♥t❡r♣r❡t t❤✐s ❛s ❡✈✐❞❡♥❝❡ ❢♦r ❛ ✭♣❡r❝❡✐✈❡❞✮ ❞✐s❝♦♥t✐♥✉✐t② ✐♥ t❤❡ ❛✉❞✐t ❢✉♥❝t✐♦♥✳ ❖✉r ♣❛♣❡r ✐s t❤❡ ✜rst t♦ q✉❛♥t✐❢② t❤❡ t❛① r❡✈❡♥✉❡ ✐♠♣❛❝t ♦❢ ✇✐t❤❤♦❧❞✐♥❣ ❢♦r ✜r♠s✱ ❛♥❞ ✐❞❡♥t✐❢② t❤❡ ✐♠♣❛❝t ♠❡❝❤❛♥✐s♠s✳ ❇② s❤♦✇✐♥❣ t❤❛t ✇✐t❤♦❧❞✐♥❣ ❡st❛❜❧✐s❤❡s ❛ ❝♦♠♣❧✐❛♥❝❡ ❞❡❢❛✉❧t✱ ✇❡ ❝♦♥tr✐❜✉t❡ t♦ t❤❡ ❜❡❤❛✈✐♦r❛❧ ❧✐t❡r❛t✉r❡ ♦♥ ❞❡❢❛✉❧ts✱ ✇❤✐❝❤ s❤♦✇s t❤❛t ❞❡❢❛✉❧ts ✐♥❝r❡❛s❡ ♦r❣❛♥ ❞♦♥❛t✐♦♥ ✭❏♦❤♥s♦♥ ✫ ●♦❧❞st❡✐♥ ✷✵✵✸✮ ❛♥❞ r❡t✐r❡♠❡♥t s❛✈✐♥❣s ✭❈❤❡tt② ❡t ❛❧✳ ✷✵✶✹✱ ❚❤❛❧❡r ✫ ❇❡♥❛rt③✐ ✷✵✵✹✱ ▼❛❞r✐❛♥ ✫ ❙❤❡❛ ✷✵✵✶✮✳ ❲❡ s❤♦✇ t❤❛t ❛ ❞❡❢❛✉❧t ❝❛♥ ❛❧s♦ ❜❡ ✉s❡❞ t♦ ✐♥❞✉❝❡ ♣❡♦♣❧❡ ✐♥t♦ ❛ ❜❡❤❛✈✐♦r t❤❛t ❡✈❡♥ r❛t✐♦♥❛❧ ❛❣❡♥ts ❞♦ ♥♦t ❞✐s♣❧❛②✳ ❚♦ t❤❡ ❡①t❡♥t t❤❛t t❤❡r❡ ♠✐❣❤t ❜❡ ❛ ❜❡❤❛✈✐♦r❛❧ ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ s♦♠❡ ♦❢ ♦✉r ✜♥❞✐♥❣s✱ ♦✉r ♣❛♣❡r ❛❧s♦ r❡❧❛t❡s t♦ t❤❡ st✉❞② ♦❢ ♦♣t✐♠❛❧ t❛①❛t✐♦♥ ✇✐t❤ ❜❡❤❛✈✐♦r❛❧ ❛❣❡♥ts ✐♥ ❋❛r❤✐ ✫ ●❛❜❛✐① ✭✷✵✶✺✮✳ ❋✐♥❛❧❧②✱ ✇❡ ❞r❛✇ ♦♥ ♠❡t❤♦❞♦❧♦❣✐❝❛❧ ❝♦♥tr✐❜✉t✐♦♥s ❢r♦♠ t✇♦ ❧✐t❡r❛t✉r❡s✳ ❲❡ ❢♦❧❧♦✇ t❤❡ ❧❡❛❞ ♦❢ ❋✐s♠❛♥ ✫ ❲❡✐ ✭✷✵✵✹✮ ✐♥ ✐❞❡♥t✐❢②✐♥❣ ♠✐sr❡♣♦rt✐♥❣ ❜② ❝♦♠♣❛r✐♥❣ t✇♦ ❞❛t❛ r❡♣♦rts ♦♥ t❤❡ s❛♠❡ t❛① ❜❛s❡✳ ❚❤✐s ❛♣♣r♦❛❝❤ ✐s ❛❧s♦ ✉s❡❞ ✐♥ ❩✉❝♠❛♥ ✭✷✵✶✸✮✱ ❑✉♠❧❡r ❘✐❥❦❡rs ❡t ❛❧✳ ✭✷✵✶✺✮✱ ❇❡st ✭✷✵✶✹✮ ❛♥❞ ❡t ❛❧✳ ✭✷✵✶✺✮✳ ❲❡ ❛❧s♦ ❞r❛✇ ♦♥ t❤❡ ❜✉♥❝❤✐♥❣ ❧✐t❡r❛t✉r❡ ✐♥ ♣✉❜❧✐❝ ✜♥❛♥❝❡✱ ✐♥✐t✐❛t❡❞ ❜② ❙❛❡③ ✭✷✵✶✵✮✱ ❈❤❡tt② ❡t ❛❧✳ ✭✷✵✶✶✮ ❛♥❞ ❑❧❡✈❡♥ ✫ ❲❛s❡❡♠ ✭✷✵✶✸✮✱ ❛♥❞ s✉♠♠❛r✐③❡❞ ✐♥ ❑❧❡✈❡♥ ✭✷✵✶✻✮✳ ❚❤✐s ❧✐t❡r❛t✉r❡ ♣r♦✈✐❞❡s t❤❡ t❡❝❤♥✐q✉❡s t♦ ❡st✐♠❛t❡ t❛①♣❛②❡rs✬ ❜❡❤❛✈✐♦r❛❧ r❡s♣♦♥s❡s t♦ ❞✐s❝♦♥t✐♥✉✐t✐❡s ✐♥ t❤❡ t❛① s❝❤❡❞✉❧❡✱ ❛♥❞ tr❛♥s❧❛t❡ t❤❡♠ ✐♥t♦ ✐♥❝♦♠❡ ❡❧❛st✐❝✐t✐❡s✳ ❚❤❡ r❡♠❛✐♥❞❡r ♦❢ t❤❡ ♣❛♣❡r ✐s ♦r❣❛♥✐③❡❞ ❛s ❢♦❧❧♦✇s✳ ❲❡ st❛rt ❜② ❞❡s❝r✐❜✐♥❣ ❛ s✐♠♣❧❡ ❝♦♥❝❡♣t✉❛❧ ❢r❛♠❡✇♦r❦ ✐♥ ❙❡❝t✐♦♥ ✷✳ ❙❡❝t✐♦♥s ✸ ❛♥❞ ✹ ♣r❡s❡♥t t❤❡ ❈♦st❛ ❘✐❝❛♥ t❛① s②st❡♠ ❛♥❞ ❞❛t❛✳ ❙❡❝t✐♦♥s ✺ ❛♥❞ ✻ ♣r❡s❡♥t t❤❡ ❛♥❛t♦♠② ♦❢ ❝♦♠♣❧✐❛♥❝❡ ❛♥❞ t❤❡ ✐♠♣❛❝t ♦❢ ✇✐t❤❤♦❧❞✐♥❣✱ ❛♥❞ s❡❝t✐♦♥ ✼ ❝♦♥❝❧✉❞❡s✳ ✷ ❈♦♥❝❡♣t✉❛❧ ❋r❛♠❡✇♦r❦ ❚❤✐s s❡❝t✐♦♥ ♣r❡s❡♥ts ❛ s✐♠♣❧❡ ❝♦♥❝❡♣t✉❛❧ ❢r❛♠❡✇♦r❦ t♦ ❛♥❛❧②③❡ ❜❡❤❛✈✐♦r❛❧ r❡s♣♦♥s❡s t♦ ✇✐t❤❤♦❧❞✐♥❣✳ ❚❤❡ ❢r❛♠❡✇♦r❦ ✐s ❜❛s❡❞ ♦♥ t❤❡ ❝❛♥♦♥✐❝❛❧ t❛① ❡✈❛s✐♦♥ ♠♦❞❡❧ ❜② ❆❧❧✐♥❣❤❛♠ ✫ ❙❛♥❞♠♦ ✭✶✾✼✷✮✱ ❡①t❡♥❞❡❞ ❜② ❑❧❡✈❡♥ ❡t ❛❧✳ ✭✷✵✶✶✮ ❛♥❞ ❈❛rr✐❧❧♦ ❡t ❛❧✳ ✭✷✵✶✹✮ t♦ ✐♥❝❧✉❞❡ t❤✐r❞✲♣❛rt② r❡♣♦rt✐♥❣ ❢♦r ✐♥❞✐✈✐❞✉❛❧s ❛♥❞ ✜r♠s r❡s♣❡❝t✐✈❡❧②✳ ❲❡ ✜rst ♣r❡s❡♥t t❤❡ ❜❛s✐❝ s❡t✉♣ ♦❢ t❤❡ ♠♦❞❡❧✱ t❤❡♥ ✐♥tr♦❞✉❝❡ ✇✐t❤❤♦❧❞✐♥❣ ✇✐t❤ ❢✉❧❧ r❡❝❧❛✐♠✱ ❛♥❞ ✜♥❛❧❧② ❝♦♥s✐❞❡r ❛ ♠♦❞❡❧ ♦❢ ✇✐t❤❤♦❧❞✐♥❣ ✇✐t❤ ❝♦st❧② r❡❝❧❛✐♠✳ ✺ ✷✳✶ ❆ ❙✐♠♣❧❡ ❚❛① ❊✈❛s✐♦♥ ▼♦❞❡❧ ❚❤❡ ❜❛s✐❝ s❡t✉♣ ♦❢ ♦✉r ♠♦❞❡❧ ❢♦❧❧♦✇s ❈❛rr✐❧❧♦ ❡t ❛❧✳ ✭✷✵✶✹✮✳ ❋✐r♠s ❤❛✈❡ r❡✈❡♥✉❡ R = RT + RS ✱ ✇❤❡r❡ r❡✈❡♥✉❡ ❝❛♥ ❜❡ ❡✐t❤❡r t❤✐r❞✲♣❛rt② r❡♣♦rt❡❞ ♦r s❡❧❢✲r❡♣♦rt❡❞✱ ✐♥❞❡①❡❞ ❜② T ❛♥❞ S ✱ ❛♥❞ ✜r♠s ❞❡❝❧❛r❡ ˆ ❋✐r♠s ❤❛✈❡ ❝♦sts C = Cs ✱ ✇❤✐❝❤ ✇❡ ❛ss✉♠❡ ❢♦r s✐♠♣❧✐❝✐t② t♦ ❜❡ ❢✉❧❧② s❡❧❢✲r❡♣♦rt❡❞✱ ❛♥❞ ✜r♠s R ˆ ❚❤❡ ❣♦✈❡r♥♠❡♥t ❧❡✈✐❡s t❛① ❛t r❛t❡ τ ♦♥ ❞❡❝❧❛r❡❞ ♣r♦✜ts π ˆ − Cˆ ✳ ❚❤❡ t❛① ❝❤♦s❡ t♦ r❡♣♦rt C ˆ =R ❧✐❛❜✐❧✐t② ✐s T = τ π ˆ ✳ ❲✐t❤ ♣r♦❜❛❜✐❧✐t② p✱ ✜r♠s ❛r❡ ❛✉❞✐t❡❞✱ ✐♥ ✇❤✐❝❤ ❝❛s❡ ❛♥② ❡✈❛s✐♦♥ ✐s ❝❡rt❛✐♥ t♦ ❜❡ ❞❡t❡❝t❡❞✱ ❛♥❞ ❡✈❛❞❡rs ♣❛② ❛ ✜♥❡ θ ✇❤✐❝❤ ✐s ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡ ❡✈❛❞❡❞ ❧✐❛❜✐❧✐t②✳ ❋✐r♠s ♠❛①✐♠✐③❡ ❡①♣❡❝t❡❞ ✉t✐❧✐t②✾ ♦✈❡r ❛❢t❡r✲t❛① ✐♥❝♦♠❡ ✐♥ t❤❡ ❛✉❞✐t❡❞ ❛♥❞ ♥♦♥✲❛✉❞✐t❡❞ st❛t❡ ♦❢ t❤❡ ✇♦r❧❞✱ YA ❛♥❞ YN ✿ EU = (1 − p)U (YN ) + pU (YA ) = (1 − p)U (π − τ π ˆ ) + pU (π − τ π − θτ (π − π ˆ )) ❚♦ t❛❦❡ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ t❛① ❛✉t❤♦r✐t✐❡s✬ ✉s❡ ♦❢ r✐s❦ s❝♦r❡s t♦ t❛r❣❡t ❛✉❞✐ts✱ ✇❡ ❢✉rt❤❡r ❢♦❧❧♦✇ ❈❛rr✐❧❧♦ ❡t ❛❧✳ ✭✷✵✶✹✮ ❜② ❛ss✉♠✐♥❣ t❤❛t t❤❡ ❛✉❞✐t ♣r♦❜❛❜✐❧✐t② ✐s ❞❡❝r❡❛s✐♥❣ ✐♥ t❤❡ r❡♣♦rt❡❞ ♣r♦✜t r❛t❡✱ ˆ ✇✐t❤ p < 0✱ ❛♥❞ ♠✐s✲r❡♣♦rt✐♥❣ ❛❣❛✐♥st t❤✐r❞✲♣❛rt② ✐♥❢♦r♠❛t✐♦♥ ❧❡❛❞s t♦ ❝❡rt❛✐♥ p = p((ˆ π + )/R) ˆ < RT ✳✶✵ ❲✐t❤ t❤❡s❡ ❛ss✉♠♣t✐♦♥✱ ✜r♠s ❝❤♦♦s❡ t♦ r❡♣♦rt R ˆ ∗ ≥ RT ✱ ❛♥❞ ❝❤♦♦s❡ ❞❡t❡❝t✐♦♥✿ p = ✐❢ R Cˆ ∗ ≷ C t♦ s❛t✐s❢② t❤❡ ✜rst✲♦r❞❡r ❝♦♥❞✐t✐♦♥✳ ❚♦ ❡♥s✉r❡ t❤❛t t❤❡ ❣♦✈❡r♥♠❡♥t ❛❧✇❛②s ♣r❡❢❡rs ❧❡ss ❡✈❛s✐♦♥✱ ✐✳❡✳ ∂R/∂ π ˆ > ✱ ✇❡ ❛ss✉♠❡ t❤❛t θ ❛♥❞ p ❛r❡ s♠❛❧❧✱ ✇❤✐❝❤ ❛r❡ r❡❛s♦♥❛❜❧❡ ❛ss✉♠♣t✐♦♥s ✐♥ ❛ ♠✐❞❞❧❡✲✐♥❝♦♠❡ ❝♦✉♥tr②✳ ❆s ✐s ❛❧s♦ st❛♥❞❛r❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✱ ✇❡ ❡♥s✉r❡ t❤❛t t❤❡ s❡❝♦♥❞✲♦r❞❡r ❝♦♥❞✐t✐♦♥ ✐s ♠❡t ❛♥❞ ❛✈♦✐❞ ♥♦♥✲❝♦♥❝❛✈✐t✐❡s ❜② ✐♠♣♦s✐♥❣ p ≥ 0✳ ✷✳✷ ❲✐t❤❤♦❧❞✐♥❣ ✇✐t❤ ❋✉❧❧ ❘❡❝❧❛✐♠ ❲❡ ✐♥tr♦❞✉❝❡ ✇✐t❤❤♦❧❞✐♥❣ ✐♥t♦ t❤❡ ♠♦❞❡❧ ❜② ❛ss✉♠✐♥❣ t❤❛t t❛① ✐s ✇✐t❤❡❧❞ ❛t ❛ r❛t❡ µ ♦♥ t❤✐r❞✲♣❛rt② r❡♣♦rt❡❞ r❡✈❡♥✉❡ RT ✳ ❚❤❡ ✐♥❢♦r♠❛t✐♦♥ r❡♣♦rt✐♥❣ ❛❣❡♥t t❤✉s ❛❧s♦ ❜❡❝♦♠❡s t❤❡ ✇✐t❤❤♦❧❞✐♥❣ ❛❣❡♥t✳ ❆s ✜r♠s ❛r❡ ❛❧r❡❛❞② ❝❤♦s✐♥❣ t♦ r❡♣♦rt r❡✈❡♥✉❡ ❧❛r❣❡r t❤❛♥ ♦r ❡q✉❛❧ t♦ t❤✐r❞✲♣❛rt② r❡♣♦rt❡❞ r❡✈❡♥✉❡✱ t❤❡ ✐♥tr♦❞✉❝t✐♦♥ ♦❢ ✇✐t❤❤♦❧❞✐♥❣ ❧❡❛✈❡s t❤❡ ✐♥❢♦r♠❛t✐♦♥ ❡♥✈✐r♦♥♠❡♥t ✉♥❝❤❛♥❣❡❞✳ ■♥ ❛ ✜rst st❡♣✱ ✇❡ ❛ss✉♠❡ t❤❛t t❤❡ t❛① ✇✐t❤❤❡❧❞ ❝❛♥ ❜❡ ❢✉❧❧② r❡❝❧❛✐♠❡❞✱ ❛s ✐s t❡❝❤♥✐❝❛❧❧② t❤❡ ❝❛s❡ ✐♥ ♠♦st ✇✐t❤❤♦❧❞✐♥❣ s②st❡♠s✳ ❚❤✐s ♠❡❛♥s t❤❛t ✜r♠s✬ ♥❡t t❛① ❧✐❛❜✐❧✐t② ❛♥❞ ❤❡♥❝❡ ♣❛②♠❡♥t ✐s P = T − µRT ✱ ✇❤❡r❡ t❤❡ t❛① ✾ ❆s ❈❛rr✐❧❧♦ ❡t ❛❧✳ ✭✷✵✶✹✮✱ ✇❡ ❝♦♥s✐❞❡r t❤❛t ♠♦❞❡❧✐♥❣ ✜r♠s ✐♥ ❛ ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr② ❝♦♥t❡①t ❛s r✐s❦✲❛✈❡rs❡ ✐s r❡❛s♦♥❛❜❧❡✱ s✐♥❝❡ ♠♦r❡ t❤❛♥ ❤❛❧❢ ♦❢ t❤❡ ✜r♠s ✐♥ ♦✉r s❛♠♣❧❡ ❛r❡ ✉♥✐♥❝♦r♣♦r❛t❡❞✱ ❛♥❞ ♠♦st ✜r♠s ❛r❡ ✈✉❧♥❡r❛❜❧❡ t♦ ✐♥❝♦♠❡ ✈♦❧❛t✐❧✐t②✳ ✶✵ ❚❤❡ ✐♥❝❧✉s✐♦♥ ♦❢ ✱ ❛ s♠❛❧❧ ♣♦s✐t✐✈❡ ♥✉♠❜❡r✱ ❡♥s✉r❡s t❤❛t ✜r♠s ❞❡❝❧❛r✐♥❣ ③❡r♦ ♣r♦✜ts ♦♥ ❛ ❧❛r❣❡ r❡✈❡♥✉❡ ❜❛s❡ ✐♥❝✉r ❛ ❤✐❣❤❡r ❛✉❞✐t ♣r♦❜❛❜✐❧✐t② t❤❛♥ ✜r♠s ❞❡❝❧❛r✐♥❣ ③❡r♦ ♣r♦✜ts ♦♥ ❛ s♠❛❧❧ r❡✈❡♥✉❡ ❜❛s❡✱ t❤✉s ❞✐✛❡r❡♥t✐❛t✐♥❣ t❤❡ t✇♦ ❝♦r♥❡r ❝❛s❡s ✇❤❡r❡ πˆ = 0✳ ✻ ✇✐t❤❤❡❧❞ ✐s ❞❡❞✉❝t❡❞ ❢r♦♠ t❤❡ ❣r♦ss t❛① ❧✐❛❜✐❧✐t②✳ ❚❤❡r❡ ❛r❡ ♥♦ r❡str✐❝t✐♦♥s ♦♥ t❤❡ s✐❣♥ ♦❢ P, P ≷ 0✱ s♦ t❤❛t ✜r♠s ❝❛♥ r❡q✉❡st ❛ r❡❢✉♥❞ ✐❢ t❤❡ r❡♣♦rt❡❞ t❛① ❧✐❛❜✐❧✐t② ✐s s♠❛❧❧❡r t❤❛♥ t❤❡ t❛① ✇✐t❤❤❡❧❞✳ ■♥ t❤✐s ♠♦❞❡❧✱ ✜r♠s✬ ❛❢t❡r✲t❛① ✐♥❝♦♠❡ ✐♥ t❤❡ ❛✉❞✐t❡❞ ❛♥❞ ♥♦♥✲❛✉❞✐t❡❞ st❛t❡ ♦❢ t❤❡ ✇♦r❧❞ ❛r❡ Y¯N = π − µRT − [τ π ˆ − µRT ] = π − τ π ˆ = YN ✱ Y¯A = π − µRT − [τ π − µRT ] − θ[(τ π − µRT ) − (τ π ˆ − µRT )] = π − τ π − θτ (π − π ˆ ) = YA ✳ ❆❢t❡r✲t❛① ✐♥❝♦♠❡ ✐♥ ❜♦t❤ st❛t❡s ✐s ❡①❛❝t❧② ❡q✉❛❧ t♦ ❛❢t❡r✲t❛① ✐♥❝♦♠❡ ✐♥ t❤❡ ♠♦❞❡❧ ✇✐t❤♦✉t ✇✐t❤✲ ❤♦❧❞✐♥❣✳ ❲✐t❤❤♦❧❞✐♥❣ ✐s t❤✉s ✐rr❡❧❡✈❛♥t t♦ ✜r♠s✬ ❡✈❛s✐♦♥ ❞❡❝✐s✐♦♥s✳ ❚❤✐s tr✐✈✐❛❧ r❡s✉❧t ♦❜✈✐♦✉s❧② r❡❧✐❡s ♦♥ t❤❡ ❛ss✉♠♣t✐♦♥ ♦❢ ❢✉❧❧ ❛♥❞ ❝♦st❧❡ss r❡❝❧❛✐♠✱ ✇❤✐❝❤ ✇❡ r❡❧❛① ✐♥ t❤❡ ♥❡①t s❡❝t✐♦♥✳✶✶ ✷✳✸ ❲✐t❤❤♦❧❞✐♥❣ ✇✐t❤ ❈♦st❧② ❘❡❝❧❛✐♠ ❚♦ ❜r✐♥❣ t❤❡ ♠♦❞❡❧ ❝❧♦s❡r t♦ r❡❛❧✐t②✱ ✇❡ ❛ss✉♠❡ t❤❛t ✜r♠s ♣❛② ❛ ✜r♠✲s♣❡❝✐✜❝ ✜①❡❞ ❝♦st fi ✱ ❞✐str✐❜✉t❡❞ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ❝✉♠✉❧❛t✐✈❡ ❞✐str✐❜✉t✐♦♥ ❢✉♥❝t✐♦♥ H(f )✱ t♦ r❡❝❧❛✐♠ t❤❡ t❛① ✇✐t❤❤❡❧❞ µRT ✳ ❚❤✐s ✜①❡❞ ❝♦st ❝❛♥ r❡♣r❡s❡♥t t❤❡ ❝♦st ♦❢ ❝♦❧❧❡❝t✐♥❣ ✇✐t❤❤♦❧❞✐♥❣ r❡❝❡✐♣ts ❢♦r ❡❛❝❤ tr❛♥s❛❝t✐♦♥ ❛♥❞ ❛❞❞✐♥❣ ✉♣ t❤❡ ❛♠♦✉♥ts ✇❤❡♥ ♣r❡♣❛r✐♥❣ t❤❡ t❛① r❡t✉r♥✳ ■t ❝❛♥ ❛❧s♦ ❝❛♣t✉r❡✱ ❛❧❜❡✐t ✐♥ ❛ ❝r✉❞❡ ✇❛②✱ t❤❡ ♠♦♥❡t❛r② ❝♦st ♦❢ ❛♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ♠♦♥✐t♦r✐♥❣ ♦r ❛✉❞✐t ♣r♦❜❛❜✐❧✐t② t❤❛t ✜r♠s ♠❛② ❢❛❝❡ ✇❤❡♥ r❡❝❧❛✐♠✐♥❣ t❛① ✇✐t❤❤❡❧❞✳✶✷ ❚❤❡ ♣r❡s❡♥❝❡ ♦❢ t❤❡ ✜①❡❞ ❝♦st ❣❡♥❡r❛t❡s ❛ ❝✉t✲♦✛ f¯ = µRT s✉❝❤ t❤❛t ✜r♠s ✇✐t❤ fi < f¯ r❡❝❧❛✐♠ t❤❡ t❛① ✇✐t❤❤❡❧❞ ❛♥❞ ✜r♠s ✇✐t❤ fi ≥ f¯ ❞♦ ♥♦t r❡❝❧❛✐♠✳ ❆ ✜rst t❡st❛❜❧❡ ♣r❡❞✐❝t✐♦♥ ♦❢ t❤❡ ♠♦❞❡❧ ✐s t❤✉s t❤❛t r❡❝❧❛✐♠ ♦❢ t❤❡ t❛① ✇✐t❤❤❡❧❞ ✐s ✐♥❝♦♠♣❧❡t❡✱ H(f¯) < 1✱ ❛♥❞ t❤❛t t❤❡ s❤❛r❡ ♦❢ r❡❝❧❛✐♠❡rs ✐♥❝r❡❛s❡s ✐♥ t❤❡ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡✱ ∂H(f¯)/∂µ > 0✳ ❈♦♠♣❛r❛t✐✈❡ ❙t❛t✐❝s ❢♦r ❋✐r♠s ❆❜s❡♥t ❛♥② ❜❡❤❛✈✐♦r❛❧ r❡s♣♦♥s❡✱ r❡❝❧❛✐♠❡rs ❡①♣❡r✐❡♥❝❡ ❛ ❞❡✲ ❝r❡❛s❡ ✐♥ t❤❡✐r ❛❢t❡r✲t❛① ✐♥❝♦♠❡ ♦❢ fi < µRT ❛♥❞ ♥♦♥✲r❡❝❧❛✐♠❡rs ❡①♣❡r✐❡♥❝❡ ❛ ❞❡❝r❡❛s❡ ♦❢ t❤❡✐r ❛❢t❡r✲t❛① ✐♥❝♦♠❡ ♦❢ µRT ❋♦r ❜♦t❤ t②♣❡s ♦❢ ✜r♠s✱ t❤❡ ❛❜s♦❧✉t❡ ❞❡❝r❡❛s❡ ✐s t❤❡ s❛♠❡ ✐♥ t❤❡ ❛✉❞✐t❡❞ ❛♥❞ ♥♦♥✲❛✉❞✐t❡❞ st❛t❡✳✶✸ ❚❛①♣❛②❡rs ❛❞❥✉st t❤❡✐r r❡♣♦rt✐♥❣ ❜❡❤❛✈✐♦r ✐♥ r❡s♣♦♥s❡ t♦ t❤❡ ❞❡❝r❡❛s❡ ✐♥ ❛❢t❡r✲t❛① ✐♥❝♦♠❡✳ ❯♥❞❡r ❞❡❝r❡❛s✐♥❣ ❛❜s♦❧✉t❡ r✐s❦ ❛✈❡rs✐♦♥✱ ❛s ✐♥ ❆❧❧✐♥❣❤❛♠ ✫ ❙❛♥❞♠♦ ✭✶✾✼✷✮✱ ♦♥❡ ❝❛♥ s❤♦✇ t❤❛t r❡❝❧❛✐♠❡rs ❞❡❝❧❛r❡ π ˆ1 ❛♥❞ ♥♦♥✲r❡❝❧❛✐♠❡rs ❞❡❝❧❛r❡ π ˆ2 ✇✐t❤ π ˆ2 >ˆ π1 > π ˆ ∗ , ✇❤❡r❡ π ˆ ∗ ✐s t❤❡ t❛①♣❛②❡rs✬ ♦♣t✐♠✉♠ ✐♥ t❤❡ ❜❛s❡❧✐♥❡ ♠♦❞❡❧ ✇✐t❤♦✉t ✇✐t❤❤♦❧❞✐♥❣✳ ■♥t✉✐t✐✈❡❧②✱ t❤❡ ❞❡❝r❡❛s❡ ✐♥ ❛❢t❡r✲t❛① ✐♥❝♦♠❡ ❤✉rts ✜r♠s ♠♦r❡ ✐♥ t❤❡ ❛✉❞✐t❡❞ st❛t❡✱ ❛♥❞ t❤✉s ✐♥❞✉❝❡s t❤❡♠ t♦ ❜❡❝♦♠❡ ♠♦r❡ ❝♦♠♣❧✐❛♥t✳ ❚❤✐s s✐♠✉❧t❛♥❡♦✉s❧② r❡❞✉❝❡s t❤❡ ❧✐❦❡❧✐❤♦♦❞ ♦❢ ❞❡t❡❝t✐♦♥ ❛♥❞ ✐♥❝r❡❛s❡s ❛❢t❡r✲t❛① ✐♥❝♦♠❡ ✐♥ t❤❡ ❝❛s❡ ✶✶ ❖t❤❡r ♥♦♥✲✐♥♦❝✉♦✉s ❛ss✉♠♣t✐♦♥s ♦❢ t❤❡ ♠♦❞❡❧ ❛r❡ t❤❡ ❛❜s❡♥❝❡ ♦❢ ❛♥ ❡①t❡♥s✐✈❡ ♠❛r❣✐♥ ❞❡❝✐s✐♦♥ ❛♥❞ t❤❡ ❢✉❧❧ ♣❛②♠❡♥t ♦❢ ❞❡❝❧❛r❡❞ ♥❡t ❧✐❛❜✐❧✐t✐❡s P ✳ ✶✷ ❚❤❡ ❧❛tt❡r ♠❡❝❤❛♥✐s♠ ❝♦✉❧❞ ❛❧s♦ ❜❡ ♠♦❞❡❧❡❞ ♠♦r❡ ❡①♣❧✐❝✐t❡❧② ❛s ❛ ❞✐s❝♦♥t✐♥✉♦✉s ✐♥❝r❡❛s❡ ✐♥ t❤❡ ❛✉❞✐t ♣r♦❜❛❜✐❧✐t② p ❢♦r r❡❝❧❛✐♠❡rs✱ ❡✳❣✳ p = ❢♦r ✜r♠s r❡❝❧❛✐♠✐♥❣ µRT > τ π ˆ ✱ ✇❤✐❝❤ ✇♦✉❧❞ ❣❡♥❡r❛t❡ ❜✉♥❝❤✐♥❣ ❛t t❤❡ t❤r❡s❤♦❧❞ ✇❤❡r❡ t❤❡ r❡♣♦rt❡❞ t❛① ❧✐❛❜✐❧✐t② ❡q✉❛❧s t❤❡ t❛① ✇✐t❤❤❡❧❞✱ ❢♦r s✉✣❝✐❡♥t❧② r✐s❦ ❛✈❡rs❡ ✜r♠s✱ ❛s s❤♦✇ ✐♥ ❈❛r✐❧❧♦ ❡t ❛❧✳ ✭✷✵✶✷✮✳ ✶✸ ❲❡ ❛ss✉♠❡ t❤❛t ♥♦♥✲r❡❝❧❛✐♠❡rs ❧♦s❡ t❤❡ ❛♠♦✉♥t ♦❢ t❛① ✇✐t❤❤❡❧❞ ❛❧s♦ ✇❤❡♥ t❤❡② ❛r❡ ❛✉❞✐t❡❞✳ ❚❤✐s ✐s tr✉❡ ✐❢ t❤❡② ❞✐❞ ♥♦t ❦❡❡♣ r❡❝❡✐♣ts r❡❝♦r❞✐♥❣ t❤❡ ❛♠♦✉♥ts ✇✐t❤❤❡❧❞✳ ✼ ♦❢ ❞❡t❡❝t✐♦♥✳ ❆s t❤❡ ❞❡❝r❡❛s❡ ✐♥ ❛❢t❡r✲t❛① ✐♥❝♦♠❡ ✐s ❧❛r❣❡r ❢♦r ♥♦♥✲r❡❝❧❛✐♠❡rs✱ t❤❡② r❡s♣♦♥❞ ♠♦r❡ str♦♥❣❧② t♦ t❤❡ ✇✐t❤❤♦❧❞✐♥❣ s❝❤❡♠❡✳✶✹ ■t ✐s tr✐✈✐❛❧ t♦ s❡❡ t❤❛t ∂ π ˆ1 /∂f > ❢♦r r❡❝❧❛✐♠❡rs✱ ✇✐t❤ µ ❜❡✐♥❣ ✐rr❡❧❡✈❛♥t✱ ❛♥❞ ∂ π ˆ2 /∂µ > ❢♦r ♥♦♥✲r❡❝❧❛✐♠❡rs✳ ❚❤❡ s❡❝♦♥❞ t❡st❛❜❧❡ ♣r❡❞✐❝t✐♦♥ ♦❢ t❤❡ ♠♦❞❡❧ ✐s t❤✉s t❤❛t ❛♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ✐♥❝r❡❛s❡s r❡♣♦rt❡❞ t❛①❛❜❧❡ ✐♥❝♦♠❡✱ ∂ π ˆ /∂µ > 0✳✶✺ ❈♦♠♣❛r❛t✐✈❡ ❙t❛t✐❝s ❢♦r t❤❡ ●♦✈❡r♥♠❡♥t ●♦✈❡r♥♠❡♥t r❡✈❡♥✉❡ G ✐s ❡q✉❛❧ t♦ t♦t❛❧ t❛① ♣❛②♠❡♥t ❜② ❛❧❧ ✜r♠s✳ ❆ss✉♠❡ ❛ ❝♦♥t✐♥✉✉♠ ♦❢ ✜r♠s ♦❢ ♠❡❛s✉r❡ ✶ ✇✐t❤ ✜①❡❞ ❝♦sts ❞✐str✐❜✉t❡❞ ❛❝❝♦r❞✐♥❣ t♦ H(f ) ❚❤❡♥ ❣♦✈❡r♥♠❡♥t r❡✈❡♥✉❡ ✐s t❤❡ ✇❡✐❣❤t❡❞ ❛✈❡r❛❣❡ ♦❢ r❡✈❡♥✉❡ ❛❝r♦ss t❤❡ ❛✉❞✐t❡❞ ❛♥❞ ♥♦♥✲ ❛✉❞✐t❡❞ st❛t❡ ♦❢ t❤❡ ✇♦r❧❞✱ ✇❤❡r❡ ✐♥ ❡❛❝❤ st❛t❡✱ ❛ ❢r❛❝t✐♦♥ H(f¯) ♦❢ ✜r♠s ❛r❡ r❡❝❧❛✐♠❡rs ✇❤♦ ♣❛② ❡①❛❝t❧② t❤❡ ❞❡❝❧❛r❡❞ ✭♦r tr✉❡✮ t❛① ❧✐❛❜✐❧✐t② ❛♥❞ t❤❡ r❡♠❛✐♥✐♥❣ ❢r❛❝t✐♦♥ (1 − H(f¯)) ♦❢ ✜r♠s ❛r❡ ♥♦♥✲ r❡❝❧❛✐♠❡rs ❢r♦♠ ✇❤♦♠ t❤❡ ❣♦✈❡r♥♠❡♥t ❝♦❧❧❡❝ts ❛ ❤✐❣❤❡r t❛① ❧✐❛❜✐❧✐t② ✐♥ ❛❞❞✐t✐♦♥ t♦ t❤❡ t❛① ✇✐t❤❤❡❧❞✿ G = (1 − p) H(f¯)[τ π ˆ1 ] + (1 − H(f¯))[τ π ˆ2 + µRT ] +p H(f¯)[τ π + θτ (π − π ˆ1 )] + (1 − H(f¯))[τ π + µRT + θτ (π − π ˆ2 )] ❚❤❡ ✐♥tr♦❞✉❝t✐♦♥ ♦❢ ✇✐t❤❤♦❧❞✐♥❣ t❤✉s ✐♥❝r❡❛s❡s ❣♦✈❡r♥♠❡♥t r❡✈❡♥✉❡ ❜♦t❤ ♠❡❝❤❛♥✐❝❛❧❧②✱ t❤r♦✉❣❤ t❤❡ ❝♦❧❧❡❝t✐♦♥ ♦❢ t❛① ✇✐t❤❤❡❧❞✱ ❛♥❞ t❤r♦✉❣❤ t❤❡ ✐♥❝r❡❛s❡ ✐♥ r❡♣♦rt❡❞ t❛① ❧✐❛❜✐❧✐t✐❡s✳✶✻ ❍♦✇❡✈❡r✱ t❤❡ s❡tt✐♥❣ ♦❢ t❤❡ r❡✈❡♥✉❡ ♠❛①✐♠✐③✐♥❣ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ µ ✐♥✈♦❧✈❡s ❛ tr❛❞❡✲♦✛✱ s♦ t❤❛t r❡✈❡♥✉❡ ♠❛② ✐♥❝r❡❛s❡ ♦r ❞❡❝r❡❛s❡ ✐♥ µ✱ ∂G/∂µ 0✳ ❖♥ t❤❡ ♦♥❡ ❤❛♥❞✱ ❛ ❤✐❣❤❡r ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ❛❧❧♦✇s t❤❡ ❣♦✈❡r♥♠❡♥t t♦ ❝♦❧❧❡❝t ♠♦r❡ r❡✈❡♥✉❡ ❢r♦♠ ♥♦♥✲r❡❝❧❛✐♠❡rs✳ ❖♥ t❤❡ ♦t❤❡r ❤❛♥❞✱ t❤❡ ❤✐❣❤❡r r❛t❡ ✐♥❞✉❝❡s ♠♦r❡ ✜r♠s t♦ ✐♥❝✉r t❤❡ ✜①❡❞ ❝♦st ❛♥❞ ❜❡❝♦♠❡ r❡❝❧❛✐♠❡rs✱ ✇❤✐❝❤ r❡❞✉❝❡s ❣♦✈❡r♥♠❡♥t r❡✈❡♥✉❡ ❛s ∂G/∂H(f¯) < 0✳ ❚❤❡ ❡✛❡❝t ♦❢ ❛ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ✐♥❝r❡❛s❡ ♦♥ ❣♦✈❡r♥♠❡♥t r❡✈❡♥✉❡ ✐s t❤✉s t❤❡♦r❡t✐❝❛❧❧② ❛♠❜✐❣✉♦✉s✳ ❲❡ ♣r♦❝❡❡❞ t♦ ❡st✐♠❛t❡ t❤✐s ❡✛❡❝t ❡♠♣✐r✐❝❛❧❧② ✉s✐♥❣ ♣♦❧✐❝② ✈❛r✐❛t✐♦♥ ✐♥ ❈♦st❛ ❘✐❝❛✳ ✸ ❚❛① ❙②st❡♠ ❈♦st❛ ❘✐❝❛✬s t❛① s②st❡♠ r❡❧✐❡s ♣r❡❞♦♠✐♥❛♥t❧② ♦♥ t❤❡ ✐♥❝♦♠❡ t❛① ❢♦r ✜r♠s ❛♥❞ t❤❡ s❛❧❡s t❛①✳ ❋✐r♠s ✐♥ ❈♦st❛ ❘✐❝❛ r❡❣✐st❡r ❡✐t❤❡r ❛s ❛s ♣❡rs♦♥❛ ❢ís✐❝❛ ✭✉♥✐♥❝♦r♣♦r❛t❡❞ ✜r♠✱ ✐✳❡✳ s❡❧❢✲❡♠♣❧♦②❡❞ ✐♥❞✐✈✐❞✉❛❧s✮ ♦r ♣❡rs♦♥❛ ❥✉rí❞✐❝❛ ✭❝♦r♣♦r❛t✐♦♥✮✱ ✉s✐♥❣ t❤❡ ❉✶✹✵ r❡❣✐str❛t✐♦♥ ❢♦r♠✳ ❚❤❡r❡ ❛r❡ ♥♦ s✐③❡ t❤r❡s❤♦❧❞s ♦r ♦t❤❡r r❡q✉✐r❡♠❡♥ts ♦❜❧✐❣✐♥❣ ✜r♠s t♦ ❝❤♦s❡ ♦♥❡ ✜r♠ t②♣❡ ♦r t❤❡ ♦t❤❡r✱ ❜✉t t❤❡ ❣♦✈❡r♥❛♥❝❡ str✉❝t✉r❡ ✶✹ ❆s ❤❛s ❜❡❡♥ s❤♦✇♥ ✐♥ t❤❡ r❡❢❡r❡♥❝❡❞ ♣❛♣❡rs✱ πˆ ❛❧s♦ ✐♥❝r❡❛s❡s ✐♥ p, θ ❛♥❞ RT ❆♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ❢r♦♠ µ1 t♦ µ2 > µ1 ✇✐❧❧ ❛❧s♦ ✐♥❞✉❝❡ s♦♠❡ ♥♦♥✲r❡❝❧❛✐♠❡rs t♦ ❜❡❝♦♠❡ r❡❝❧❛✐♠❡rs✳ ❍♦✇❡✈❡r✱ t❤❡s❡ ✜r♠s ✇✐❧❧ st✐❧❧ ❡①♣❡r✐❡♥❝❡ ❛ ❞❡❝r❡❛s❡ ✐♥ t❤❡✐r ❛❢t❡r✲t❛① ✐♥❝♦♠❡ ❜② fi − µ1 RT ✱ ❛s µ1 RT < fi < µ2 RT ❢♦r t❤❡♠✱ s♦ t❤❛t t❤❡② ✇✐❧❧ ❛❧s♦ ❝❤♦s❡ t♦ ✐♥❝r❡❛s❡ r❡♣♦rt❡❞ t❛①❛❜❧❡ ✐♥❝♦♠❡✳ ✶✻ ❚❤✐s r❡s✉❧t ✇♦✉❧❞ ❜❡ str❡♥❣t❤❡♥❡❞ ✐♥ ❛ ❝♦♥t❡①t ♦❢ ❡①t❡♥s✐✈❡ ❝♦♠♣❧✐❛♥❝❡ ❣❛♣s ♦r ✉♥❞❡r✲♣❛②♠❡♥t ♦❢ ❧✐❛❜✐❧✐t✐❡s✳ ✶✺ ✽ ❋✐❣✉r❡ ❱■✿ P❛②♠❡♥t ♦❢ ❚❛① ▲✐❛❜✐❧✐t✐❡s Average Payment Share 85 95 Average Payment Share of Net Liability, Income Tax 2006 2008 2010 Year Self-Employed, cut 04-2015 Self-Employed, cut 04-2013 Self-Employed, cut 04-2011 2012 2014 Corporations, cut 04-2015 Corporations, cut 04-2013 Corporations, cut 04-2011 75 Average Payment Share 85 95 Average Payment Share of Net Liability, Sales Tax 2009m1 2010m7 2012m1 Month Self-Employed, cut 04-2015 Self-Employed, cut 04-2013 Self-Employed, cut 04-2011 2013m7 2015m1 Corporations, cut 04-2015 Corporations, cut 04-2013 Corporations, cut 04-2011 ◆♦t❡s✿ ❚❤✐s ✜❣✉r❡ s❤♦✇s t❤❡ ❛✈❡r❛❣❡ ♦❢ t❤❡ ♣❛②♠❡♥t s❤❛r❡✱ ❞❡✜♥❡❞ ❛s t❤❡ t♦t❛❧ ♣❛②♠❡♥t ♠❛❞❡ ❜② t❤❡ t❛①♣❛②❡r ❢♦r ❛ s♣❡❝✐✜❝ t❛① ♣❡r✐♦❞✱ ❞✐✈✐❞❡❞ ❜② t❤❡ ✜♥❛❧ t❛① ❧✐❛❜✐❧✐t② t♦ ❜❡ ♣❛✐❞ ❢♦r t❤❛t ♣❡r✐♦❞✳ ❚❤❡ ❛✈❡r❛❣❡ ✐s ❛♥ ✉♥✇❡✐❣❤t❡❞ ❛✈❡r❛❣❡ ❛❝r♦ss ❛❧❧ t❛①♣❛②❡rs ✇✐t❤ ❛♥ ♣♦s✐t✐✈❡ ✜♥❛❧ ❧✐❛❜✐❧✐t② ❢♦r ❡❛❝❤ ✜s❝❛❧ ♣❡r✐♦❞✳ ❚❤❡ ✜♥❛❧ t❛① ❧✐❛❜✐❧✐t② ✐s ♥❡t ♦❢ ❛♥② ❞❡❞✉❝t✐♦♥ ♠❛❞❡ ❢♦r t❛① ✇✐t❤❤❡❧❞✱ ❛♥❞ t❤❡ ♣❛②♠❡♥t ❞❛t❛ ❞♦❡s ♥♦t ✐♥❝❧✉❞❡ t❛① ✇✐t❤❤❡❧❞✳ ❚❤❡ ✐♥❝♦♠❡ t❛① ❞❛t❛ ✐♥❝❧✉❞❡s ❛❧❧ ❞❡❝❧❛r❛t✐♦♥s ✜❧❡❞ ❛♥❞ ♣❛②♠❡♥ts ♠❛❞❡ ❜② ❏✉♥❡ ✷✵✶✺✳ ❚❤❡ s❛❧❡s t❛① ❞❛t❛ ✐♥❝❧✉❞❡s ❛❧❧ ❞❡❝❧❛r❛t✐♦♥s ✜❧❡❞ ❛♥❞ ♣❛②♠❡♥ts ♠❛❞❡ ❜② ❖❝t♦❜❡r ✷✵✶✺✳ ❚❤❡ ❜❧✉❡ s❡r✐❡s ❝♦rr❡s♣♦♥❞ t♦ t❤❡ s❡❧❢✲❡♠♣❧♦②❡❞ ❛♥❞ t❤❡ r❡❞ s❡r✐❡s ❝♦rr❡s♣♦♥❞s t♦ ❝♦r♣♦r❛t✐♦♥s✳ ❲❡ s❤♦✇ t❤❡ s❡r✐❡s ❢♦r t❤r❡❡ ❞✐✛❡r❡♥t ❝✉ts ✐♥ t❤❡ ♣❛②♠❡♥ ❞❛t❛✱ t❛❦✐♥❣ ✐♥t♦ ❛❝❝♦✉♥t ❛❧❧ ♣❛②♠❡♥ts ♠❛❞❡ ❜❡❢♦r❡ t❤❡ ❝✉t ❞❛t❡✳ ✸✼ ❋✐❣✉r❡ ❱■■✿ ❇✉♥❝❤✐♥❣✱ ■♥❢♦r♠❛t✐♦♥ ❘❡♣♦rt✐♥❣ ❛♥❞ ❲✐t❤❤♦❧❞✐♥❣ Self-Employed Subject to Information Reporting 0035 006 008 Self-Employed Not Subject to Information Reporting/Withholding Excess mass b=2.08(.17) Self-Employed Subject to Withholding Excess mass b=1.19(.19) 002 0015 002 001 Observed distribution 150 50 Counterfactual 100 Taxable Income/Kink (%) Observed distribution Corporations Not Subject to Information Reporting/Withholding 002 Excess mass b=4.49(.47) 150 50 Counterfactual 100 Taxable Income/Kink (%) Observed distribution Corporations Subject to Information Reporting Excess mass b=3.17(.21) 150 Counterfactual Corporations Subject to Withholding 002 100 Taxable Income/Kink (%) Missing mass m=.23(.07) Density 0025 Density 003 004 Density 004 002 50 0008 Missing mass m=.75(.08) Missing mass m=-.14(.06) 003 006 005 Excess mass b=4.5(.3) 100 Total Revenue/Notch (%) Observed distribution 150 Counterfactual Density Missing mass m=.72(.25) 001 50 100 Total Revenue/Notch (%) Observed distribution 150 Counterfactual 0005 0005 50 0015 Density 001 0015 Density 0004 Missing mass m=1.07(.2) 0002 ✸✽ 0006 Excess mass b=1.33(.27) Missing mass m=3.65(1.01) 50 100 Total Revenue/Notch (%) Observed distribution 150 Counterfactual ◆♦t❡s✿ ❚❤❡ ✜❣✉r❡ s❤♦✇s t❤❡ ❞❡♥s✐t② ❞✐str✐❜✉t✐♦♥ ♦❢ t❛①❛❜❧❡ ✐♥❝♦♠❡ ❢♦r t❤❡ s❡❧❢✲❡♠♣❧♦②❡❞ ❛r♦✉♥❞ t❤❡ ✜rst ❦✐♥❦ ✐♥ t❤❡ ✐♥❝♦♠❡ t❛① s❝❤❡❞✉❧❡ ✭t♦♣ r♦✇✮✱ ❛♥❞ t❤❡ ❞❡♥s✐t② ❞✐str✐❜✉t✐♦♥ ♦❢ t♦t❛❧ r❡✈❡♥✉❡ ❢♦r ❝♦r♣♦r❛t✐♦♥s ❛r♦✉♥❞ t❤❡ ✜rst ♥♦t❝❤ ✐♥ t❤❡ ❝♦r♣♦r❛t✐♦♥ t❛① s❝❤❡❞✉❧❡ ✭❜♦tt♦♠ r♦✇✮✳ ❚❤❡ ❞❛t❛ ✐s ♣♦♦❧❡❞ ❢♦r ②❡❛rs ✷✵✵✻✲✷✵✶✹✱ r❡♣r❡s❡♥t❡❞ ❛s ♣❡r❝❡♥t❛❣❡ ❞✐st❛♥❝❡ ❢r♦♠ t❤❡ ❦✐♥❦✱ ❛♥❞ ❛❣❣r❡❣❛t❡❞ ✐♥ t❛①❛❜❧❡ ✐♥❝♦♠❡ ❜✐♥s ♦❢ ✶✪✳ ❚❤❡ ♣❛♥❡❧s s❤♦✇ t❤❡ ❞✐str✐❜✉t✐♦♥ ❢♦r ❞✐✛❡r❡♥t s✉❜s❛♠♣❧❡s✱ ❛s ✐♥❞✐❝❛t❡❞ ❜② t❤❡ ♣❛♥❡❧ t✐t❧❡s✳ ❚❤❡ ❜❧✉❡ ❞♦tt❡❞ ❧✐♥❡ ♠❛r❦s t❤❡ ❡♠♣✐r✐❝❛❧ ❞✐str✐❜✉t✐♦♥✱ t❤❡ r❡❞ s♦❧✐❞ ❧✐♥❡ ♠❛r❦s t❤❡ ❝♦✉♥t❡r❢❛❝t✉❛❧✱ ✜tt❡❞ ❛s ❛ ✢❡①✐❜❧❡ ♣♦❧②♥♦♠✐❛❧ t♦ t❤❡ ♦❜s❡r✈❡❞ ❞✐str✐❜✉t✐♦♥ ♦✉ts✐❞❡ t❤❡ ❡①❝❧✉❞❡❞ r❛♥❣❡✳ ❲❡ ✉s❡ ❛♥ ❡✐❣❤t❤✲❞❡❣r❡❡ ♣♦❧②♥♦♠✐❛❧ ❢♦r s❡❧❢✲❡♠♣❧♦②❡❞ ❛♥❞ ❛ s✐①t❤✲❞❡❣r❡❡ ♣♦❧②♥♦♠✐❛❧ ❢♦r ❝♦r♣♦r❛t✐♦♥s✳ ❚❤❡ ❡①❝❧✉❞❡❞ r❛♥❣❡ ❛❜♦✈❡ t❤❡ t❤r❡s❤♦❧❞ ❝♦✈❡rs ❢♦✉r ❛♥❞ s❡✈❡♥ ❜✐♥s r❡s♣❡❝t✐✈❡❧② ✐♥ t❤❡ t✇♦ ❣r♦✉♣s ♦❢ ✜r♠s✳ ❚❤❡ ❡①❝❡ss ♠❛ss b ❛♥❞ ♠✐ss✐♥❣ ♠❛ss m ❛r❡ ❡st✐♠❛t❡❞ ❛s t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ♦❜s❡r✈❡❞ ❛♥❞ ❡st✐♠❛t❡❞ ❞❡♥s✐t②✱ ✇❡✐❣❤t❡❞ ❜② t❤❡ ❤❡✐❣❤t ♦❢ t❤❡ ❝♦✉♥t❡r❢❛❝t✉❛❧ ❞❡♥s✐t②✳ ❚❤❡ st❛♥❞❛r❞ ❡rr♦rs ❛r❡ ❜♦♦tstr❛♣♣❡❞✳ ❋✐❣✉r❡ ❱■■■✿ ❊✈❡♥t ❙t✉❞② ♦❢ ❘❡♣♦rt✐♥❣ ❇❡❤❛✈✐♦r Corporations Change in Taxable Income 1.5 Change in Taxable Income 1.5 2.5 Reporting by Other Firms (D151 Sales) Self-Employed 2.5 Reporting by Other Firms (D151 Sales) DD=.058 (.114) 5 DD=.182 (.027) -4 -3 -2 -1 Event Year Control Group -4 -3 Event Group -2 -1 Event Year Control Group Event Group Withholding by State (D150) Self-Employed Corporations Change in Taxable Income 1.5 Change in Taxable Income 1.5 2.5 Withholding by State (D150) 2.5 DD=.253 (.045) 5 DD=.425 (.069) -4 -3 -2 -1 Event Year Control Group -4 -3 Event Group -2 -1 Event Year Control Group Event Group Reporting by Credit/Debit Card Company (D153) Self-Employed Corporations Change in Taxable Income 1.5 Change in Taxable Income 1.5 2.5 Reporting by Credit/Debit Card Company (D153) 2.5 DD=.211 (.048) 5 DD=.442 (.133) -4 -3 -2 -1 Event Year Control Group -4 Event Group -3 -2 -1 Event Year Control Group Event Group ◆♦t❡s✿ ❚❤❡ ✜❣✉r❡s ❞✐s♣❧❛② t❤❡ ❝❤❛♥❣❡ ✐♥ t❛① ❧✐❛❜✐❧✐t②✱ ❝♦♠♣❛r❡❞ t♦ t❤❡ ♣r❡✲❡✈❡♥t ❛✈❡r❛❣❡ ♦❢ t❤❡ ❡✈❡♥t ❛♥❞ ❝♦♥tr♦❧ ❣r♦✉♣✱ ❢♦r ❡✈❡♥t ②❡❛rs ✲✹ t♦ ✸✳ ❚❤❡ ❡✈❡♥t ❣r♦✉♣ ✐♥❝❧✉❞❡s ✜r♠s t❤❛t r❡❝❡✐✈❡ ❛ ✜rst ✐♥❢♦r♠❛t✐✈❡ ❞❡❝❧❛r❛t✐♦♥ ✐♥ ❡✈❡♥t ②❡❛r ✵✳ ❊✈❡♥t ②❡❛rs ❝♦♥s✐❞❡r❡❞ ✐♥ t❤✐s ❡st✐♠❛t✐♦♥ ❛r❡ ✷✵✶✵ ❛♥❞ ✷✵✶✶✱ ❛♥❞ ❝♦♥tr♦❧ ✜r♠s ❛r❡ ❛❧❧ ✜r♠s t❤❛t ❤❛✈❡ ♥♦t r❡❝❡✐✈❡❞ ❛ ✜rst ✐♥❢♦r♠❛t✐✈❡ ❞❡❝❧❛r❛t✐♦♥ ❜② t❤❡ ❡✈❡♥t ②❡❛r✳ ❚❤❡ ❧❡❢t ❝♦❧✉♠♥ ✐s ❢♦r t❤❡ s❡❧❢✲❡♠♣❧♦②❡❞✱ t❤❡ r✐❣❤t ❝♦❧✉♠♥ ✐s ❢♦r ❝♦r♣♦r❛t✐♦♥s✳ P❛♥❡❧ ❆ ❝♦♥s✐❞❡rs t❤❡ r❡❝❡✐♣t ♦❢ ❛ ✜rst ✐♥❢♦r♠❛t✐✈❡ ❞❡❝❧❛r❛t✐♦♥ ❢r♦♠ ❛♥♦t❤❡r ✜r♠ ✭✐♥❢♦r♠❛t✐♦♥ r❡♣♦rt✐♥❣ ♦♥❧②✮✱ ♣❛♥❡❧ ❇ ❝♦♥s✐❞❡rs t❤❡ r❡❝❡✐♣t ♦❢ ❛ ✜rst ✐♥❢♦r♠❛t✐✈❡ ❞❡❝❧❛r❛t✐♦♥ ❢r♦♠ ❛ st❛t❡ ✐♥st✐t✉t✐♦♥ ✭✐♥❢♦r♠❛t✐♦♥ r❡♣♦rt✐♥❣ ❛♥❞ ✇✐t❤❤♦❧❞✐♥❣✮✱ ❛♥❞ ♣❛♥❡❧ ❈ ❝♦♥s✐❞❡rs t❤❡ r❡❝❡✐♣t ♦❢ ❛ ✜rst ✐♥❢♦r♠❛t✐✈❡ ❞❡❝❧❛r❛t✐♦♥ ❢r♦♠ ❛ ❝r❡❞✐❞✴❞❡❜✐t ❝❛r❞ ❝♦♠♣❛♥② ✭✐♥❢♦r♠❛t✐♦♥ r❡♣♦rt✐♥❣ ❛♥❞ ✇✐t❤❤♦❧❞✐♥❣✮✳ ❚❤❡ t❡①t ❞✐s♣❧❛②s t❤❡ ❞✐✛❡r❡♥❝❡✲✐♥✲❞✐✛❡r❡♥❝❡ ❡st✐♠❛t❡ ❢r♦♠ ❡q✉❛t✐♦♥ ✶✳ ✸✾ ❋✐❣✉r❡ ■❳✿ ❲✐t❤❤♦❧❞✐♥❣ ❘❛t❡ ❘❡❢♦r♠ Average Withholding Base 8000 9000 10000 11000 2.5 Average Rate 7000 1.5 2009m1 2010m1 2011m1 Month N Sales Tax Declarations 2012m1 25000 2013m1 2010m1 2011m7 Month 2013m1 2014m7 53 Matching of Sales Tax and Withholding Declarations 51 52 Share Withholding 49 N Sales Tax 60000 65000 30000 35000 N Withholding 70000 Number of Sales Tax and Withholding Declarations 2008m7 27 2014m7 Share Sales Tax 24 25 26 2013m1 23 2011m7 Month 40000 2010m1 22 2008m7 55000 Withholding Base 12000 Withholding Rate 2009m1 2010m1 2011m1 Month 2012m1 2013m1 Share Sales Tax Declarations Matched With Withholding Share Withholding Declarations Matched With Tax Declaration N Withholding Declarations ◆♦t❡s✿ ❚❤❡ ✜❣✉r❡ ❞✐s♣❧❛②s t❤❡ ❛✈❡r❛❣❡ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ❛♠♦♥❣ ✜r♠s s✉❜❥❡❝t t♦ ✇✐t❤❤♦❧❞✐♥❣ ✭♣❛♥❡❧ ❆✮✱ t❤❡ ❛✈❡r❛❣❡ ✇✐t❤❤♦❧❞✐♥❣ ❜❛s❡ ✭❝r❡❞✐t✴❞❡❜✐t ❝❛r❞ s❛❧❡s✮ ❛♠♦♥❣ t❤♦s❡ ✜r♠s ✭♣❛♥❡❧ ❇✮✱ t❤❡ t♦t❛❧ ♥✉♠❜❡r ♦❢ s❛❧❡s t❛① ❛♥❞ ✇✐t❤❤♦❧❞✐♥❣ ❞❡❝❧❛r❛t✐♦♥s ♣❡r ♠♦♥t❤ ✭♣❛♥❡❧ ❈✮✱ ❛♥❞ t❤❡ s❤❛r❡ ♦❢ s❛❧❡s t❛① ❞❡❝❧❛r❛t✐♦♥s ♠❛t❝❤❡❞ ✇✐t❤ ❛t ❧❡❛st ♦♥❡ ✇✐t❤❤♦❧❞✐♥❣ ❞❡❝❧❛r❛t✐♦♥✱ ❛♥❞ ✈✐❝❡ ✈❡rs❛ ✭♣❛♥❡❧ ❉✮✳ ❚❤❡ ❜❧❛❝❦ s♦❧✐❞ ❧✐♥❡ ♠❛r❦s ✵✽✴✷✵✶✶✱ ✇❤❡♥ t❤❡ ✐♥❝r❡❛s❡ ✐♥ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡s ❡♥t❡r❡❞ ✐♥t♦ ❡✛❡❝t✳ ❚❤❡ ✜❣✉r❡s s❤♦✇ t❤❛t t❤❡ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ✐♥❝r❡❛s❡ ✇❛s ♥♦t ❛❝❝♦♠♣❛♥✐❡❞ ❜② ❛ ❞✐s❝♦♥t✐♥✉♦✉s ❝❤❛♥❣❡ ✐♥ t❤❡ ❛✈❡r❛❣❡ ✇✐t❤❤♦❧❞✐♥❣ ❜❛s❡✱ t❤❡ ♥✉♠❜❡r ♦❢ s❛❧❡s t❛① ♦r ✇✐t❤❤♦❧❞✐♥❣ ❞❡❝❧❛r❛t✐♦♥s✱ ❛♥❞ ♦♥❧② ❛ ♠♦❞❡st ✐♥❝r❡❛s❡ ✐♥ t❤❡ ❧✐❦❡❧✐❤♦♦❞ t❤❛t ❛ t❛①♣❛②❡r ❝♦✈❡r❡❞ ❜② ✇✐t❤❤♦❧❞✐♥❣ ✜❧❡s ❤❡r s❛❧❡s t❛① ❞❡❝❧❛r❛t✐♦♥✳ ✹✵ ❋✐❣✉r❡ ❳✿ ■♠♣❛❝t ♦❢ ❲✐t❤❤♦❧❞✐♥❣ ❘❛t❡ ■♥❝r❡❛s❡ 2.5 Total Payment Change 1.5 DD=.412 (.025) 2010m1 2011m1 Date 2012m1 Treatment Group (Rate Increase) 2013m1 Control Group Total Payment: Impact by Treatment Strength DD=.940 (.058) 1.5 Change DD=.384 (.034) DD=.294 (.031) 2010m1 2011m1 Date T: 1-2 pp Increase T: 5-6 pp Increase 2012m1 2013m1 T: 3-4 pp Increase Control Group ◆♦t❡s✿ ❚❤❡ ✜❣✉r❡ ❞✐s♣❧❛②s t❤❡ r❡s✉❧ts ♦❢ t❤❡ ❞✐✛❡r❡♥❝❡✲✐♥✲❞✐✛❡r❡♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ ❊q✉❛t✐♦♥ ✷✱ ✇✐t❤ t♦t❛❧ t❛① ♣❛②♠❡♥t ❛s ♦✉t❝♦♠❡ ✈❛r✐❛❜❧❡✳ ❚❤❡ ✜rst ♣❛♥❡❧ ❝♦♥s✐❞❡rs t❤❡ ♦✈❡r❛❧❧ ✐♠♣❛❝t ♦❢ t❤❡ r❡❢♦r♠✱ ♣♦♦❧✐♥❣ ❛❧❧ ✜r♠s ✇✐t❤ ❛ ♣r❡❞✐❝t❡❞ r❛t❡ ✐♥❝r❡❛s❡ ✐♥ t❤❡ tr❡❛t♠❡♥t ❣r♦✉♣✳ ❚❤❡ s❡❝♦♥❞ ♣❛♥❡❧ ❝♦♥s✐❞❡rs t❤❡ ✐♠♣❛❝t ♦❢ t❤❡ r❡❢♦r♠ ❜② tr❡❛t♠❡♥t str❡♥❣t❤✱ ❞✐st✐♥❣✉✐s❤✐♥❣ ✜r♠s ✇✐t❤ ❛ ♣r❡❞✐❝t❡❞ r❛t❡ ✐♥❝r❡❛s❡ ♦❢ ✶✲✷✱ ✸✲✹ ❛♥❞ ✺✲✻ ♣❡r❝❡♥t❛❣❡ ♣♦✐♥ts✳ ❚❤❡ ❝♦♥tr♦❧ ❣r♦✉♣ ✐♥❝❧✉❞❡s ✜r♠s ❡①♣❡r✐❡♥❝✐♥❣ ♥♦ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ♣r❡❞✐❝t❡❞ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ❛♥❞ ✜r♠s ♥♦t s✉❜❥❡❝t t♦ ✇✐t❤❤♦❧❞✐♥❣✳ ❚❤❡ ❜❧❛❝❦ s♦❧✐❞ ❧✐♥❡ ♠❛r❦s ✵✽✴✷✵✶✶✱ ✇❤❡♥ t❤❡ ✐♥❝r❡❛s❡ ✐♥ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡s ❡♥t❡r❡❞ ✐♥t♦ ❡✛❡❝t✳ ❚❤❡ ❞❛t❛ ✐s ✇✐♥s♦r✐③❡❞ ❜② t❤❡ ✾✾t❤ ♣❡r❝❡♥t✐❧❡✱ ❛♥❞ s❝❛❧❡❞ ❜② t❤❡ ♣r❡✲r❡❢♦r♠ ❛✈❡r❛❣❡✳ ❚❤❡ t❡①t ❞✐s♣❧❛②s t❤❡ ❝♦❡✣❝✐❡♥t β ✭♠❛r❣✐♥❛❧ ❡✛❡❝t ❝♦♠♣❛r❡❞ t♦ ♣r❡✲r❡❢♦r♠ ❛✈❡r❛❣❡✮ ❢r♦♠ ❡st✐♠❛t✐♥❣ ❊q✉❛t✐♦♥ ✷✳ ✹✶ ❋✐❣✉r❡ ❳■✿ ▼❡❝❤❛♥✐s♠s ♦❢ ❲✐t❤❤♦❧❞✐♥❣ ❘❛t❡ ■♠♣❛❝t ▼❡❝❤❛♥✐s♠ ✶✿ ■♥❝♦♠♣❧❡t❡ ❘❡❝❧❛✐♠ Share of Withheld Tax Reclaimed Share 45 Share 55 1.1 65 1.2 Reclaimers over Withholdees 2010m1 2011m1 Date 2012m1 2013m1 2010m1 2011m1 Date 2012m1 2013m1 ▼❡❝❤❛♥✐s♠ ✷✿ ❘❡❞✉❝❡❞ ▼✐s✲❘❡♣♦rt✐♥❣ 1.3 Sales Tax Collected 1.2 Input Tax Credits DD=.007 (.007) 8 9 Change Change 1.1 1.1 1.2 DD=-.02 (.009) 2010m1 2011m1 Date 2012m1 Treatment Group (Rate Increase) 2013m1 2010m1 Control Group 2011m1 Date 2012m1 Treatment Group (Rate Increase) 2013m1 Control Group Gross Tax Liability Change 1.5 DD=.116 (.017) 2010m1 2011m1 Date 2012m1 Treatment Group (Rate Increase) 2013m1 Control Group ◆♦t❡s✿ ❚❤❡ ✜❣✉r❡ ❞✐s♣❧❛②s ❡✈✐❞❡♥❝❡ ♦♥ t❤❡ ♠❡❝❤❛♥✐s♠s ❢♦r t❤❡ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ✐♠♣❛❝t✳ ■♥ ❛❧❧ ♣❛♥❡❧s✱ t❤❡ ❜❧❛❝❦ s♦❧✐❞ ❧✐♥❡ ♠❛r❦s ✵✽✴✷✵✶✶✱ ✇❤❡♥ t❤❡ ✐♥❝r❡❛s❡ ✐♥ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡s ❡♥t❡r❡❞ ✐♥t♦ ❡✛❡❝t✳ P❛♥❡❧s ❆ ❛♥❞ ❇ ❞✐s♣❧❛②✱ ❢♦r ❛❧❧ ✜r♠s s✉❜❥❡❝t t♦ ✇✐t❤❤♦❧❞✐♥❣ ✐♥ ❛ ❣✐✈❡♥ ♠♦♥t❤✱ t❤❡ s❤❛r❡ ♦❢ ✜r♠s ♠❛❦✐♥❣ ❛ r❡❝❧❛✐♠✱ ❛♥❞ t❤❡ ❛✈❡r❛❣❡ s❤❛r❡ ♦❢ ✇✐t❤❤❡❧❞ t❛① r❡❝❧❛✐♠❡❞✳ ❚❤❡ s❤❛r❡s ❛r❡ ✇✐♥s♦r✐③❡❞ ❜② t❤❡ ✾✾✳✾t❤ ♣❡r❝❡♥t✐❧❡✳ P❛♥❡❧s ❈✱ ❉ ❛♥❞ ❊ s❤♦✇ r❡s✉❧ts ♦❢ t❤❡ ❞✐✛❡r❡♥❝❡✲✐♥✲❞✐✛❡r❡♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ ❊q✉❛t✐♦♥ ✷✱ ✇✐t❤ ❞✐✛❡r❡♥t ♦✉t❝♦♠❡ ✈❛r✐❛❜❧❡s✱ ❛s ✐♥❞✐❝❛t❡❞ ❜② t❤❡ ✜❣✉r❡ t✐t❧❡s✳ ❚❤❡ tr❡❛t♠❡♥t ❣r♦✉♣ ✐♥❝❧✉❞❡s ✜r♠s ❡①♣❡r✐❡♥❝✐♥❣ ❛♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ♣r❡❞✐❝t❡❞ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ✐♥ ✵✽✴✷✵✶✶✱ t❤❡ ❝♦♥tr♦❧ ❣r♦✉♣ ✐♥❝❧✉❞❡s ✜r♠s ❡①♣❡r✐❡♥❝✐♥❣ ♥♦ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ♣r❡❞✐❝t❡❞ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ ❛♥❞ ✜r♠s ♥♦t s✉❜❥❡❝t t♦ ✇✐t❤❤♦❧❞✐♥❣✳ ❚❤❡ ❞❛t❛ ✐s ✇✐♥s♦r✐③❡❞ ❜② t❤❡ ✾✾t❤ ♣❡r❝❡♥t✐❧❡✱ ❛♥❞ s❝❛❧❡❞ ❜② t❤❡ ♣r❡✲✵✾✴✷✵✶✶ ❛✈❡r❛❣❡✳ ❚❤❡ t❡①t ❞✐s♣❧❛②s t❤❡ ❝♦❡✣❝✐❡♥t β ✭♠❛r❣✐♥❛❧ ❡✛❡❝t ❝♦♠♣❛r❡❞ t♦ ♣r❡✲r❡❢♦r♠ ❛✈❡r❛❣❡✮ ❢r♦♠ ❡st✐♠❛t✐♥❣ ❊q✉❛t✐♦♥ ✷✳ ✹✷ ❋✐❣✉r❡ ❳■■✿ ❆❣❣r❡❣❛t❡ ■♠♣❛❝t Pre-Reform Mean: RD: 4.73 (1.13) 49.5 bio CRC -5 Revenue Demeaned (Bio Col) 10 15 Total Sales Tax Revenue (Official Statistics) 2008m1 2010m1 2012m1 Month Tax Revenue 2014m1 2016m1 Linear Fit ◆♦t❡s✿ ❚❤✐s ✜❣✉r❡ s❤♦✇s t❤❡ ✐♠♣❛❝t ♦❢ t❤❡ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡ r❡❢♦r♠ ✐♥ ❆✉❣✉st ✷✵✶✶ ♦♥ ❛❣❣r❡❣❛t❡ s❛❧❡s t❛① r❡✈❡♥✉❡✳ ❚❤❡ ❞♦ts r❡♣r❡s❡♥t ♠♦♥t❤❧② s❛❧❡s t❛① r❡✈❡♥✉❡ ✐♥ ❜✐❧❧✐♦♥s ♦❢ ❈♦st❛ ❘✐❝❛♥ ❝♦❧♦♥❡s✱ ❛s ♣❡r t❤❡ ♦✣❝✐❛❧ st❛t✐st✐❝s✳ ❚❤❡ r❡❞ ❧✐♥❡ ✐s ❛ ❧✐♥❡❛r ✜t✱ ❛❧❧♦✇✐♥❣ ❢♦r ❛ ❞✐s❝♦♥t✐♥✉✐t② ❛t t❤❡ t✐♠❡ ♦❢ t❤❡ r❡❢♦r♠✳ ❚❤❡ t❡①t ❞✐s♣❧❛②s t❤❡ ❝♦❡✣❝✐❡♥t ❛♥❞ st❛♥❞❛r❞ ❡rr♦r ♦♥ t❤❡ ♣♦st✲r❡❢♦r♠ ❞✉♠♠②✳ ❚❤❡ r❡s✉❧ts ❛r❡ r♦❜✉st t♦ ♦♠✐tt✐♥❣ ♦r ❝♦♥tr♦❧❧✐♥❣ ❢♦r t❤❡ ♦✉t❧✐❡r ♠♦♥t❤s ♦❢ ❉❡❝❡♠❜❡r ❛♥❞ ❏❛♥✉❛r②✳ ✹✸ ❆♣♣❡♥❞✐① ❋✐❣✉r❡ ❳■■■✿ P❛②♠❡♥t ♦❢ ❚❛① ▲✐❛❜✐❧✐t✐❡s Share Paid Share of Net Tax Liability Paid, Income Tax 2006 2008 Year 2010 Total Share, Self-Employed Mean Share, Self-Employed 2012 Total Share, Corporations Mean Share, Corporations Share Paid Share of Net Tax Liability Paid, Sales Tax 2009m7 2010m7 2011m7 2012m7 Month Total Share, Self-Employed Mean Share, Self-Employed 2013m7 2014m7 Total Share, Corporations Mean Share, Corporations ◆♦t❡s✿ ❚❤✐s ✜❣✉r❡ ❡①t❡♥❞s ❋✐❣✉r❡ ❱■✱ ❞✐s♣❧❛②✐♥❣ ❛❞❞✐t✐♦♥❛❧❧② t❤❡ s❤❛r❡ ♦❢ t♦t❛❧ t❛① ♣❛②♠❡♥ts ♠❛❞❡ ❜② t❤❡ t❛①♣❛②❡rs ♦✈❡r t❤❡ t♦t❛❧ ✜♥❛❧ t❛① ❧✐❛❜❧✐t②✳ ❆❧❧ ✈❛r✐❛❜❧❡ ❞❡✜♥✐t✐♦♥s ❛r❡ ❛s ✐♥ t❤❡ ♥♦t❡s t♦ ❋✐❣✉r❡ ❱■✳ ❙❡❡ ❙❡❝t✐♦♥ ✺✳✸ ❢♦r ❛ ❞✐s❝✉ss✐♦♥ ♦❢ t❤❡s❡ r❡s✉❧ts✳ ✹✹ ❋✐❣✉r❡ ❳■❱✿ ❘♦❜✉st♥❡ss ♦❢ ❲✐t❤❤♦❧❞✐♥❣ ■♠♣❛❝t P❛♥❡❧ ❇✿ P❛②❡rs ❛♥❞ ❩❡r♦✲▲✐❛❜✐❧✐t② ❋✐r♠s 2.2 P❛♥❡❧ ❆✿ ❙❡❧❢✲❊♠♣❧♦②❡❞ DD=.465 (.025) Change 1.5 7 1 1.5 Change 2.2 DD=.857 (.045) 2010m1 2011m1 Date 2012m1 Treatment Group (Rate Increase) 2013m1 2010m1 Control Group 2011m1 Date 2012m1 Treatment Group (Rate Increase) 2013m1 Control Group P❛♥❡❧ ❈✿ P❛②❡rs ❖♥❧② 2.2 Total Payment Change 1.5 DD=.353 (.039) 2010m1 2011m1 Date 2012m1 Treatment Group (Rate Increase) 2013m1 Control Group ◆♦t❡s✿ ❚❤✐s ✜❣✉r❡ r❡♣❧✐❝❛t❡s ❋✐❣✉r❡ ❳✱ ❧✐♠✐t✐♥❣ t❤❡ s❛♠♣❧❡ t♦ t❤❡ s❡❧❢✲❡♠♣❧♦②❡❞ ✭♣❛♥❡❧ ❆✮✱ ✜r♠s ✇✐t❤ ③❡r♦ ♥❡t ❧✐❛❜✐❧✐t② ♦r ♥♦♥✲③❡r♦ ✭♦✇♥✮ t❛① ♣❛②♠❡♥t ✭♣❛♥❡❧ ❇✮✱ ❛♥❞ ✜r♠s ♠❛❦✐♥❣ ❛ ♥♦♥✲③❡r♦ ✭♦✇♥✮ t❛① ♣❛②♠❡♥t ✭♣❛♥❡❧ ❈✮✳ ✹✺ ❋✐❣✉r❡ ❳❱✿ ■♠♣❛❝t ✐❢ ■♥❝♦♠❡ ❚❛① ❲✐t❤❤♦❧❞✐♥❣ ❢♦r ❋✐r♠s 1.4 Gross Tax Liability Year-on-Year Change 1.2 DD=.237 (.018) Introduction of CIT WH 2008 2010 Year 2012 Treatment Group (Withholdees) 2014 2015 Control Group ◆♦t❡s✿ ❚❤✐s ✜❣✉r❡ s❤♦✇s t❤❡ ✐♠♣❛❝t ♦❢ t❤❡ ✐♥tr♦❞✉❝t✐♦♥ ♦♥ ✇✐t❤❤♦❧❞✐♥❣ ❢♦r t❤❡ ✐♥❝♦♠❡ t❛① ✐♥ ✷✵✶✺ ✭❝♦r♣♦r❛t✐♦♥ ❛♥❞ s❡❧❢✲❡♠♣❧♦②❡❞✮ ♦♥ r❡♣♦rt❡❞ ❣r♦ss t❛① ❧✐❛❜✐❧✐t②✱ ✉s✐♥❣ ❛ ❞✐✛❡r❡♥❝❡✲✐♥✲❞✐✛❡r❡♥❝❡ ❡st✐♠❛t✐♦♥✳ ✹✻ ❘❡❢❡r❡♥❝❡s ❆❧❧✐♥❣❤❛♠✱ ▼✐❝❤❛❡❧ ●✳✱ ✫ ❙❛♥❞♠♦✱ ❆❣♥❛r✳ ✶✾✼✷✳ ■♥❝♦♠❡ ❚❛① ❊✈❛s✐♦♥✿ ❆ ❚❤❡♦r❡t✐❝❛❧ ❆♥❛❧✲ ②s✐s✳ ❏♦✉r♥❛❧ ♦❢ P✉❜❧✐❝ ❊❝♦♥♦♠✐❝s✱ ✶✱ ✸✷✸✕✸✸✽✳ ❆❧♠✉♥✐❛✱ ▼✐❣✉❡❧✱ ✫ ❘♦❞r✐❣✉❡③✱ ❉❛✈✐❞ ▲♦♣❡③✳ ✷✵✶✺✳ ❯♥❞❡r t❤❡ ❘❛❞❛r✿ ❚❤❡ ❊✛❡❝ts ♦❢ ▼♦♥✐✲ t♦r✐♥❣ ❋✐r♠s ♦♥ ❚❛① ❈♦♠♣❧✐❛♥❝❡✳ ❇❛❝❤❛s✱ P✐❡rr❡✳ ✷✵✶✺✳ ❙♦❝✐❛❧ ❙❝✐❡♥❝❡ ❘❡s❡❛r❝❤ ◆❡t✇♦r❦✱ ❆✉❣✉st✳ ◆♦t✭❝❤✮ ❨♦✉r ❆✈❡r❛❣❡ ❚❛① ❙②st❡♠✿ ❈♦r♣♦r❛t❡ ❚❛①❛t✐♦♥ ❯♥❞❡r ❲❡❛❦ ❊♥✲ ❢♦r❝❡♠❡♥t✳ ▼✐♠❡♦✳ ❇❛rr✱ ▼✐❝❤❛❡❧ ❙✳✱ ✫ ❉♦❦❦♦✱ ❏❛♥❡ ❑✳ ✷✵✵✽✳ P❛②✐♥❣ t♦ s❛✈❡✿ t❛① ✇✐t❤❤♦❧❞✐♥❣ ❛♥❞ ❛ss❡t ❛❧❧♦❝❛t✐♦♥ ❛♠♦♥❣ ❧♦✇✲ ❛♥❞ ♠♦❞❡r❛t❡✲✐♥❝♦♠❡ t❛①♣❛②❡rs✳ ❋✐♥❛♥❝❡ ❛♥❞ ❊❝♦♥♦♠✐❝s ❉✐s❝✉ss✐♦♥ ❙❡r✐❡s ✷✵✵✽✲✶✶✳ ❇♦❛r❞ ♦❢ ●♦✈❡r♥♦rs ♦❢ t❤❡ ❋❡❞❡r❛❧ ❘❡s❡r✈❡ ❙②st❡♠ ✭❯✳❙✳✮✳ ❇❡s❧❡②✱ ❚✐♠♦t❤② ❏✳✱ ✫ P❡rss♦♥✱ ❚♦rst❡♥✳ ✷✵✶✸ ✭❏❛♥✳✮✳ ❚❛①❛t✐♦♥ ❛♥❞ ❉❡✈❡❧♦♣♠❡♥t✳ ❈❊P❘ ❉✐s❝✉ss✐♦♥ P❛♣❡rs ✾✸✵✼✳ ❈✳❊✳P✳❘✳ ❉✐s❝✉ss✐♦♥ P❛♣❡rs✳ ❇❡st✱ ▼✐❝❤❛❡❧✱ ❇r♦❝❦♠❡②❡r✱ ❆♥♥❡✱ ❑❧❡✈❡♥✱ ❍❡♥r✐❦✱ ❙♣✐♥♥❡✇✐❥♥✱ ❏♦❤❛♥♥❡s✱ ✫ ❲❛s❡❡♠✱ ▼❛③❤❛r✳ ✷✵✶✺✳ Pr♦❞✉❝t✐♦♥ ✈s ❘❡✈❡♥✉❡ ❊✣❝✐❡♥❝② ✇✐t❤ ▲♦✇ ❚❛① ❈♦♠♣❧✐❛♥❝❡✿ ❚❤❡♦r② ❛♥❞ ❊✈✐✲ ❞❡♥❝❡ ❢r♦♠ P❛❦✐st❛♥✳ ❏♦✉r♥❛❧ ♦❢ P♦❧✐t✐❝❛❧ ❊❝♦♥♦♠②✱ ✶✷✸✭✻✮✱ ✶✸✶✶✕✶✸✺✺✳ ❇❡st✱ ▼✐❝❤❛❡❧ ❈❛r❧♦s✳ ✷✵✶✹✳ ❙❛❧❛r② ▼✐sr❡♣♦rt✐♥❣ ❛♥❞ t❤❡ ❘♦❧❡ ♦❢ ❋✐r♠s ✐♥ ❲♦r❦❡rs✬ ❘❡s♣♦♥s❡s t♦ ❚❛①❡s✿ ❊✈✐❞❡♥❝❡ ❢r♦♠ P❛❦✐st❛♥✳ ▼✐♠❡♦✳ ❇❡st✱ ▼✐❝❤❛❡❧ ❈❛r❧♦s✱ ✫ ❑❧❡✈❡♥✱ ❍❡♥r✐❦ ❏❛❝♦❜s❡♥✳ ✷✵✶✺✳ ❍♦✉s✐♥❣ ▼❛r❦❡t ❘❡s♣♦♥s❡s t♦ ❚r❛♥s❛❝t✐♦♥ ❚❛①❡s✿ ❊✈✐❞❡♥❝❡ ❢r♦♠ ◆♦t❝❤❡s ❛♥❞ ❙t✐♠✉❧✉s ✐♥ t❤❡ ❯❑✳ ▼✐♠❡♦✳ ❇r♦❝❦♠❡②❡r✱ ❆♥♥❡✳ ✷✵✶✹✳ ❑✐♥❦✳ ❚❤❡ ■♥✈❡st♠❡♥t ❊✛❡❝t ♦❢ ❚❛①❛t✐♦♥✿ ❊✈✐❞❡♥❝❡ ❢r♦♠ ❛ ❈♦r♣♦r❛t❡ ❚❛① ❋✐s❝❛❧ ❙t✉❞✐❡s✱ ✸✺✭✹✮✱ ✹✼✼✕✺✵✾✳ ❇r♦❝❦♠❡②❡r✱ ❆♥♥❡✱ ❍❡r♥❛♥❞❡③✱ ▼❛r❝♦✱ ❙♠✐t❤✱ ❙♣❡♥❝❡r✱ ✫ ❑❡tt❧❡✱ ❙t❡✇❛rt✳ ✷✵✶✺✳ ❈❛st✐♥❣ t❤❡ ❚❛① ◆❡t ❲✐❞❡r✿ ❊①♣❡r✐♠❡♥t❛❧ ❊✈✐❞❡♥❝❡ ❢r♦♠ ❈♦st❛ ❘✐❝❛✳ ▼✐♠❡♦✳ ❇r✉❤♥✱ ▼✐r✐❛♠✱ ✫ ▼❝❑❡♥③✐❡✱ ❉❛✈✐❞✳ ✷✵✶✹✳ ❝r♦❡♥t❡r♣r✐s❡s ✐♥ ❉❡✈❡❧♦♣✐♥❣ ❈♦✉♥tr✐❡s✳ ❊♥tr② ❘❡❣✉❧❛t✐♦♥ ❛♥❞ t❤❡ ❋♦r♠❛❧✐③❛t✐♦♥ ♦❢ ▼✐✲ ❲♦r❧❞ ❇❛♥❦ ❘❡s❡❛r❝❤ ❖❜s❡r✈❡r✱ ✷✾✭✷✮✱ ✶✽✻✕✷✵✶✳ ❈❛r✐❧❧♦✱ P❛✉❧✱ ❊♠r❛♥✱ ❙❤❛❤❡✱ ✫ ❘✐✈❛❞❡♥❡✐r❛✱ ❆♥✐t❛✳ ✷✵✶✷✳ Pr♦✜t t❛①❡s✱ ✇✐t❤❤♦❧❞✐♥❣ r❛t❡s ❛♥❞ t❛① ❡✈❛s✐♦♥✳ ▼✐♠❡♦✳ ✹✼ ❉♦ ❝❤❡❛t❡rs ❜✉♥❝❤ t♦❣❡t❤❡r❄ ❈❛rr✐❧❧♦✱ P❛✉❧✱ P♦♠❡r❛♥③✱ ❉✐♥❛✱ ✫ ❙✐♥❣❤❛❧✱ ▼♦♥✐❝❛✳ ✷✵✶✹✳ ❚❛① ▼❡ ✐❢ ❨♦✉ ❈❛♥✿ ❊✈✐❞❡♥❝❡ ♦♥ ❋✐r♠ ▼✐sr❡♣♦rt✐♥❣ ❇❡❤❛✈✐♦r ❛♥❞ ❊✈❛s✐♦♥ ❙✉❜st✐t✉t✐♦♥✳ ❲♦r❦✐♥❣ P❛♣❡r✱ ❍❛r✈❛r❞ ❯♥✐✈❡rs✐t②✳ ❈❤❡tt②✱ ❘❛❥✱ ❋r✐❡❞♠❛♥✱ ❏♦❤♥✱ ❖❧s❡♥✱ ❚♦r❡✱ ✫ P✐st❛❢❡rr✐✱ ▲✉✐❣✐✳ ✷✵✶✶✳ ❆❞❥✉st♠❡♥t ❈♦sts✱ ❋✐r♠ ❘❡s♣♦♥s❡s✱ ❛♥❞ ▼✐❝r♦ ✈s✳ ▼❛❝r♦ ▲❛❜♦r ❙✉♣♣❧② ❊❧❛st✐❝✐t✐❡s✿ ❊✈✐❞❡♥❝❡ ❢r♦♠ ❉❛♥✐s❤ ❚❛① ❘❡❝♦r❞s✳ ◗✉❛rt❡r❧② ❏♦✉r♥❛❧ ♦❢ ❊❝♦♥♦♠✐❝s✱ ✶✷✻✱ ✼✹✾✕✽✵✹✳ ❈❤❡tt②✱ ❘❛❥✱ ❋r✐❡❞♠❛♥✱ ❏♦❤♥ ◆✳✱ ▲❡t❤✲P❡t❡rs❡♥✱ ❙➹➸r❡♥✱ ◆✐❡❧s❡♥✱ ❚♦r❜❡♥ ❍❡✐❡♥✱ ✫ ❖❧s❡♥✱ ❚♦r❡✳ ✷✵✶✹✳ ❆❝t✐✈❡ ✈s✳ P❛ss✐✈❡ ❉❡❝✐s✐♦♥s ❛♥❞ ❈r♦✇❞✲❖✉t ✐♥ ❘❡t✐r❡♠❡♥t ❙❛✈✐♥❣s ❆❝❝♦✉♥ts✿ ❊✈✐❞❡♥❝❡ ❢r♦♠ ❉❡♥♠❛r❦✳ ❚❤❡ ◗✉❛rt❡r❧② ❏♦✉r♥❛❧ ♦❢ ❊❝♦♥♦♠✐❝s✱ ✶✷✾✭✸✮✱ ✶✶✹✶✕✶✷✶✾✳ ❞❡ ▼❡❧✱ ❙✉r❡s❤✱ ▼❝❑❡♥③✐❡✱ ❉❛✈✐❞✱ ✫ ❲♦♦❞r✉❢❢✱ ❈❤r✐st♦♣❤❡r✳ ✷✵✶✸✳ ❆♠❡r✐❝❛♥ ❊❝♦♥♦♠✐❝ ❛♥❞ ❈♦♥s❡q✉❡♥❝❡s ♦❢✱ ❋♦r♠❛❧✐③❛t✐♦♥ ❛♠♦♥❣ ■♥❢♦r♠❛❧ ❋✐r♠s ✐♥ ❙r✐ ▲❛♥❦❛✳ ❏♦✉r♥❛❧✿ ❆♣♣❧✐❡❞ ❊❝♦♥♦♠✐❝s✱ ✺✭✷✮✱ ✶✷✷✕✺✵✳ ❉❡❧ ❈❛r♣✐♦✱ ▲✉❝✐❛✳ ✷✵✶✹✳ ❚❤❡ ❉❡♠❛♥❞ ❢♦r✱ ❆r❡ t❤❡ ◆❡✐❣❤❜♦rs ❈❤❡❛t✐♥❣❄ ❊✈✐❞❡♥❝❡ ❢r♦♠ ❙♦❝✐❛❧ ◆♦r♠ ❊①♣❡r✐♠❡♥t ♦♥ Pr♦♣❡rt② ❚❛①❡s ✐♥ P❡r✉✳ ▼✐♠❡♦✳ ❉❡✈❡r❡✉①✱ ▼✐❝❤❛❡❧ P✳✱ ▲✐✉✱ ▲✐✱ ✫ ▲♦r❡t③✱ ❙✐♠♦♥✳ ✷✵✶✹✳ ❚❤❡ ❊❧❛st✐❝✐t② ♦❢ ❈♦r♣♦r❛t❡ ❚❛①❛❜❧❡ ■♥❝♦♠❡✿ ◆❡✇ ❊✈✐❞❡♥❝❡ ❢r♦♠ ❯❑ ❚❛① ❘❡❝♦r❞s✳ ✻✭✷✮✱ ✶✾✕✺✸✳ ❆♠❡r✐❝❛♥ ❊❝♦♥♦♠✐❝ ❏♦✉r♥❛❧✿ ❊❝♦♥♦♠✐❝ P♦❧✐❝②✱ ❉✐◆❛r❞♦✱ ❏♦❤♥✱ ❋♦rt✐♥✱ ◆✐❝♦❧❡ ▼✳✱ ✫ ▲❡♠✐❡✉①✱ ❚❤♦♠❛s✳ ✶✾✾✻✳ ▲❛❜♦r ▼❛r❦❡t ■♥st✐t✉t✐♦♥s ❛♥❞ t❤❡ ❉✐str✐❜✉t♦✐♥ ♦❢ ❲❛❣❡s✱ ✶✾✼✸✲✶✾✾✷✿ ❆ ❙❡♠✐♣❛r❛♠❡tr✐❝ ❆♣♣r♦❛❝❤✳ ❊❝♦♥♦♠❡tr✐❝❛✱ ✻✹✭✺✮✱ ✶✵✵✶✕✶✵✹✹✳ ❋❛r❤✐✱ ❊♠♠❛♥✉❡❧✱ ✫ ●❛❜❛✐①✱ ❳❛✈✐❡r✳ ✷✵✶✺ ✭❙❡♣t✳✮✳ ❖♣t✐♠❛❧ ❚❛①❛t✐♦♥ ✇✐t❤ ❇❡❤❛✈✐♦r❛❧ ❆❣❡♥ts✳ ◆❇❊❘ ❲♦r❦✐♥❣ P❛♣❡rs ✷✶✺✷✹✳ ◆❛t✐♦♥❛❧ ❇✉r❡❛✉ ♦❢ ❊❝♦♥♦♠✐❝ ❘❡s❡❛r❝❤✱ ■♥❝✳ ❋✐s♠❛♥✱ ❘❛②♠♦♥❞✱ ✫ ❲❡✐✱ ❙❤❛♥❣✲❏✐♥✳ ✷✵✵✹✳ ✫q✉♦t❀▼✐ss✐♥❣ ■♠♣♦rts✫q✉♦t❀ ✐♥ ❈❤✐♥❛✳ ❚❛① ❘❛t❡s ❛♥❞ ❚❛① ❊✈❛s✐♦♥✿ ❊✈✐❞❡♥❝❡ ❢r♦♠ ❏♦✉r♥❛❧ ♦❢ P♦❧✐t✐❝❛❧ ❊❝♦♥♦♠②✱ ✶✶✷✭✷✮✱ ✹✼✶✕✺✵✵✳ ●❛♥❞❤✐✱ ❆s❤✈✐♥✱ ✫ ❑✉❡❤❧✇❡✐♥✱ ▼✐❝❤❛❡❧✳ ✷✵✶✹✳ ❘❡❡①❛♠✐♥✐♥❣ ■♥❝♦♠❡ ❚❛① ❖✈❡r✇✐t❤❤♦❧❞✐♥❣ ❛s ❛ ❘❡s♣♦♥s❡ t♦ ❯♥❝❡rt❛✐♥t②✳ P✉❜❧✐❝ ❋✐♥❛♥❝❡ ❘❡✈✐❡✇✳ ●♦r❞♦♥✱ ❘♦❣❡r✱ ✫ ▲✐✱ ❲❡✐✳ ✷✵✵✾✳ ♣♦ss✐❜❧❡ ❡①♣❧❛♥❛t✐♦♥✳ ❚❛① str✉❝t✉r❡s ✐♥ ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr✐❡s✿ ▼❛♥② ♣✉③③❧❡s ❛♥❞ ❛ ❏♦✉r♥❛❧ ♦❢ P✉❜❧✐❝ ❊❝♦♥♦♠✐❝s✱ ✾✸✭✼✲✽✮✱ ✽✺✺✕✽✻✻✳ ✹✽ ❍✐❣❤❢✐❧❧✱ ❏❛♥♥❡tt✱ ❚❤♦rs♦♥✱ ❉♦✉❣❧❛s✱ ✫ ❲❡❜❡r✱ ❲✐❧❧✐❛♠ ❱✳ ✶✾✾✽✳ ❚❛① ❖✈❡r✇✐t❤❤♦❧❞✐♥❣ ❛s ❛ ❘❡s♣♦♥s❡ ❚♦ ❯♥❝❡rt❛✐♥t②✳ ❍✐❧❣❡r✱ ◆❛t❤❛♥✐❡❧ ●✳ ✷✵✶✹✳ P✉❜❧✐❝ ❋✐♥❛♥❝❡ ❘❡✈✐❡✇✱ ✷✻✭✹✮✱ ✸✼✻✕✸✾✶✳ P❛r❡♥t❛❧ ❏♦❜ ▲♦ss ❛♥❞ ❈❤✐❧❞r❡♥✬s ▲♦♥❣✲❚❡r♠ ❖✉t❝♦♠❡s✿ ❊✈✐❞❡♥❝❡ ❢r♦♠ ✼ ▼✐❧❧✐♦♥ ❋❛t❤❡rs✬ ▲❛②♦✛s✳ ▼✐♠❡♦✳ ■❘❙✳ ✷✵✶✷✳ ❚❛① ❨❡❛r ✷✵✵✻ ❚❛① ●❛♣ ❊st✐♠❛t❡s✳ ❚❡❝❤✳ r❡♣t✳ ■♥t❡r♥❛❧ ❘❡✈❡♥✉❡ ❙❡r✈✐❝❡✳ ❋❙✲✷✵✶✷✲✻✳ ❏♦❤♥s♦♥✱ ❊r✐❝ ❏✳✱ ✫ ●♦❧❞st❡✐♥✱ ❉❛♥✐❡❧✳ ✷✵✵✸✳ ❉♦ ❉❡❢❛✉❧ts ❙❛✈❡ ▲✐✈❡s❄ ❙❝✐❡♥❝❡✱ ✸✵✷✭✺✻✹✾✮✱ ✶✸✸✽✕✶✸✸✾✳ ❑❡❡♥✱ ▼✐❝❤❛❡❧✳ ✷✵✵✽✳ ❱❆❚✱ t❛r✐✛s✱ ❛♥❞ ✇✐t❤❤♦❧❞✐♥❣✿ ❇♦r❞❡r t❛①❡s ❛♥❞ ✐♥❢♦r♠❛❧✐t② ✐♥ ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr✐❡s✳ ❏♦✉r♥❛❧ ♦❢ P✉❜❧✐❝ ❊❝♦♥♦♠✐❝s✱ ✾✷✭✶✵✲✶✶✮✱ ✶✽✾✷✕✶✾✵✻✳ ❑❧❡✈❡♥✱ ❍❡♥r✐❦✳ ✷✵✶✻✳ ❇✉♥❝❤✐♥❣✳ ❆♥♥✉❛❧ ❘❡✈✐❡✇ ♦❢ ❊❝♦♥♦♠✐❝s✱ ❢♦rt❤❝♦♠✐♥❣✱ ✽✳ ❑❧❡✈❡♥✱ ❍❡♥r✐❦ ❏✳✱ ✫ ❲❛s❡❡♠✱ ▼❛③❤❛r✳ ✷✵✶✸✳ ❯s✐♥❣ ◆♦t❝❤❡s t♦ ❯♥❝♦✈❡r ❖♣t✐♠✐③❛t✐♦♥ ❋r✐❝✲ t✐♦♥s ❛♥❞ ❙tr✉❝t✉r❛❧ ❊❧❛st✐❝✐t✐❡s✿ ❚❤❡♦r② ❛♥❞ ❊✈✐❞❡♥❝❡ ❢r♦♠ P❛❦✐st❛♥✳ ❊❝♦♥♦♠✐❝s✱ ✶✷✽✱ ✻✻✾✕✼✷✸✳ ◗✉❛rt❡r❧② ❏♦✉r♥❛❧ ♦❢ ❑❧❡✈❡♥✱ ❍❡♥r✐❦ ❏❛❝♦❜s❡♥✱ ❑♥✉❞s❡♥✱ ▼❛rt✐♥ ❇✳✱ ❑r❡✐♥❡r✱ ❈❧❛✉s ❚❤✉str✉♣✱ P❡❞❡rs❡♥✱ ❙ør❡♥✱ ✫ ❙❛❡③✱ ❊♠♠❛♥✉❡❧✳ ✷✵✶✶✳ ❯♥✇✐❧❧✐♥❣ ♦r ❯♥❛❜❧❡ t♦ ❈❤❡❛t❄ ❊✈✐❞❡♥❝❡ ❋r♦♠ ❛ ❚❛① ❆✉❞✐t ❊①♣❡r✐♠❡♥t ✐♥ ❉❡♥♠❛r❦✳ ❊❝♦♥♦♠❡tr✐❝❛✱ ✼✾✭✸✮✱ ✻✺✶✕✻✾✷✳ ❑❧❡✈❡♥✱ ❍❡♥r✐❦ ❏❛❝♦❜s❡♥✱ ❑r❡✐♥❡r✱ ❈❧❛✉s ❚❤✉str✉♣✱ ✫ ❙❛❡③✱ ❊♠♠❛♥✉❡❧✳ ✷✵✶✺✳ ❲❤② ❈❛♥ ▼♦❞❡r♥ ●♦✈❡r♥♠❡♥ts ❚❛① ❙♦ ▼✉❝❤❄ ❆♥ ❆❣❡♥❝② ▼♦❞❡❧ ♦❢ ❋✐r♠s ❛s ❋✐s❝❛❧ ■♥t❡r♠❡❞✐❛r✐❡s✳ ▼✐♠❡♦✳ ❑♦♣❝③✉❦✱ ❲♦❥❝✐❡❝❤✱ ✫ ❙❧❡♠r♦❞✱ ❏♦❡❧✳ ✷✵✵✻✳ P✉tt✐♥❣ ❋✐r♠s ✐♥t♦ ❖♣t✐♠❛❧ ❚❛① ❚❤❡♦r②✳ ❆♠❡r✲ ✐❝❛♥ ❊❝♦♥♦♠✐❝ ❘❡✈✐❡✇ P❛♣❡rs ❛♥❞ Pr♦❝❡❡❞✐♥❣s✱ ✾✻✭✷✮✱ ✶✸✵✕✶✸✹✳ ❑✉♠❧❡r✱ ❚♦❞❞✱ ❱❡r❤♦♦❣❡♥✱ ❊r✐❝✱ ✫ ❋rí❛s✱ ❏✉❞✐t❤ ❆✳ ✷✵✶✺✳ ❊♥❧✐st✐♥❣ ❲♦r❦❡rs ✐♥ ■♠♣r♦✈✐♥❣ P❛②r♦❧❧✲❚❛① ❈♦♠♣❧✐❛♥❝❡✿ ❊✈✐❞❡♥❝❡ ❢r♦♠ ▼❡①✐❝♦✳ ◆❇❊❘ ❲♦r❦✐♥❣ P❛♣❡r ✶✾✸✽✺✳ ▼❛❞r✐❛♥✱ ❇r✐❣✐tt❡ ❈✳✱ ✫ ❙❤❡❛✱ ❉❡♥♥✐s ❋✳ ✷✵✵✶✳ P❛rt✐❝✐♣❛t✐♦♥ ❛♥❞ ❙❛✈✐♥❣s ❇❡❤❛✈✐♦r✳ ❚❤❡ P♦✇❡r ♦❢ ❙✉❣❣❡st✐♦♥✿ ■♥❡rt✐❛ ✐♥ ✹✵✶✭❦✮ ❚❤❡ ◗✉❛rt❡r❧② ❏♦✉r♥❛❧ ♦❢ ❊❝♦♥♦♠✐❝s✱ ✶✶✻✭✹✮✱ ✶✶✹✾✕✶✶✽✼✳ ◆❛r✐t♦♠✐✱ ❏♦❛♥❛✳ ✷✵✶✺✳ ❈♦♥s✉♠❡rs ❛s ❚❛① ❆✉❞✐t♦rs✳ ▼✐♠❡♦✳ ✹✾ ❖❊❈❉✳ ✷✵✵✾✳ ❲✐t❤❤♦❧❞✐♥❣ ❛♥❞ ✐♥❢♦r♠❛t✐♦♥ r❡♣♦rt✐♥❣ r❡❣✐♠❡s ❢♦r s♠❛❧❧ ♦r ♠❡❞✐✉♠✲s✐③❡❞ ❜✉s✐♥❡ss❡s ❛♥❞ s❡❧❢✲❡♠♣❧♦②❡❞ t❛①♣❛②❡rs✱ ■♥❢♦r♠❛t✐♦♥ ◆♦t❡✳ ❚❡❝❤✳ r❡♣t✳ ❖❊❈❉✳ P♦♠❡r❛♥③✱ ❉✐♥❛✳ ✷✵✶✺✳ t❤❡ ❱❛❧✉❡ ❆❞❞❡❞ ❚❛①✳ ◆♦ ❚❛①❛t✐♦♥ ✇✐t❤♦✉t ■♥❢♦r♠❛t✐♦♥✿ ❉❡t❡rr❡♥❝❡ ❛♥❞ ❙❡❧❢✲❊♥❢♦r❝❡♠❡♥t ✐♥ ❆♠❡r✐❝❛♥ ❊❝♦♥♦♠✐❝ ❘❡✈✐❡✇✱ ✶✵✺✭✽✮✱ ✷✺✸✾✕✷✺✻✾✳ ❘✐❥❦❡rs✱ ❇♦❜✱ ❇❛❣❤❞❛❞✐✱ ▲❡✐❧❛✱ ✫ ❘❛❜❛❧❧❛♥❞✱ ●❛❡❧ ❏✳ ❘✳ ❋✳ ✷✵✶✺ ✭❏✉♥❡✮✳ P♦❧✐t✐❝❛❧ ❝♦♥♥❡❝✲ t✐♦♥s ❛♥❞ t❛r✐✛ ❡✈❛s✐♦♥ ✿ ❡✈✐❞❡♥❝❡ ❢r♦♠ ❚✉♥✐s✐❛✳ P♦❧✐❝② ❘❡s❡❛r❝❤ ❲♦r❦✐♥❣ P❛♣❡r ❙❡r✐❡s ✼✸✸✻✳ ❚❤❡ ❲♦r❧❞ ❇❛♥❦✳ ❙❛❡③✱ ❊♠♠❛♥✉❡❧✳ ✷✵✶✵✳ ❉♦ ❚❛①♣❛②❡rs ❇✉♥❝❤ ❛t ❑✐♥❦ P♦✐♥ts❄ ❊❝♦♥♦♠✐❝ P♦❧✐❝②✱ ✷✭✸✮✱ ✶✽✵✕✷✶✷✳ ❙❛♠❛♥❛♠✉❞✱ ❊♥r✐q✉❡✳ ✷✵✶✸✳ ❆♠❡r✐❝❛♥ ❊❝♦♥♦♠✐❝ ❏♦✉r♥❛❧✿ ❊st✉❞✐♦ ❝♦♠♣❛r❛❞♦ ❞❡ ❧♦s r❡❣✐♠❡♥❡s ❞❡ r❡t❡♥❝✐♦♥❡s ② ♣❡r❝❡♣❝✐♦♥❡s ❞❡❧ ■❱❆ ❡ ✐♠♣✉❡st♦ ❛ ❧❛ r❡♥t❛ ❡♥ ❆♠❡r✐❝❛ ▲❛t✐♥❛ ② ❡❧ ❈❛r✐❜❡✳ ❚❡❝❤✳ r❡♣t✳ ■♥t❡r✲❆♠❡r✐❝❛♥ ❈❡♥tr❡ ♦❢ ❚❛① ❆❞♠✐♥✐str❛t✐♦♥s✳ ❙❡✐♠✱ ❉❛✈✐❞✳ ✷✵✶✺✳ ❇❡❤❛✈✐♦r❛❧ ❘❡s♣♦♥s❡s t♦ ❛♥ ❆♥♥✉❛❧ ❲❡❛❧t❤ ❚❛①✿ ❊✈✐❞❡♥❝❡ ❢r♦♠ ❙✇❡❞❡♥✳ ▼✐♠❡♦✳ ❙❧❡♠r♦❞✱ ❏♦❡❧ ❇✳✱ ❈♦❧❧✐♥s✱ ❇r❡tt✱ ❍♦♦♣❡s✱ ❏❡❢❢r❡② ▲✳✱ ❘❡❝❦✱ ❉❛♥✐❡❧ ❍✳✱ ✫ ❙❡❜❛s✲ t✐❛♥✐✱ ▼✐❝❤❛❡❧✳ ✷✵✶✺✳ ❉♦❡s ❈r❡❞✐t✲❈❛r❞ ■♥❢♦r♠❛t✐♦♥ ❘❡♣♦rt✐♥❣ ■♠♣r♦✈❡ ❙♠❛❧❧✲❇✉s✐♥❡ss ❚❛① ❈♦♠♣❧✐❛♥❝❡❄ ▼✐♠❡♦✳ ❙♦♦s✱ P✐r♦s❦♦✳ ✶✾✾✵✳ ❙❡❧❢✲❡♠♣❧♦②❡❞ ❡✈❛s✐♦♥ ❛♥❞ t❛① ✇✐t❤❤♦❧❞✐♥❣✿ ❛ ❝♦♠♣❛r❛t✐✈❡ st✉❞② ❛♥❞ ❛♥❛❧②s✐s ♦❢ t❤❡ ✐ss✉❡s✳ ❯❈ ❉❛✈✐s ▲❛✇ ❘❡✈✐❡✇✱ ✷✹✭✶✵✼✮✱ ✶✵✼✕✶✾✸✳ ❚❤❛❧❡r✱ ❘✐❝❤❛r❞✱ ✫ ❇❡♥❛rt③✐✱ ❙❤❧♦♠♦✳ ✷✵✵✹✳ ♥♦♠✐❝s t♦ ✐♥❝r❡❛s❡ ❡♠♣❧♦②❡❡ s❛✈✐♥❣✳ ❙❛✈❡ ♠♦r❡ t♦♠♦rr♦✇✿ ❯s✐♥❣ ❜❡❤❛✈✐♦r❛❧ ❡❝♦✲ ❚❤❡ ❏♦✉r♥❛❧ ♦❢ P♦❧✐t✐❝❛❧ ❊❝♦♥♦♠②✱ ✶✶✷✭✶✮✱ ✶✻✹✕✶✽✼✳ ❯♥✐t❡❞ ◆❛t✐♦♥s✳ ✷✵✶✹✳ ▼❡❛s✉r✐♥❣ ❚❛① ❚r❛♥s❛❝t✐♦♥s ❈♦sts ✐♥ ❙♠❛❧❧ ❛♥❞ ▼❡❞✐❛♥ ❊♥t❡r♣r✐s❡s✳ ❚❡❝❤✳ r❡♣t✳ ❯♥✐t❡❞ ◆❛t✐♦♥s ❛♥❞ ■♥t❡r✲❆♠❡r✐❝❛♥ ❈❡♥tr❡ ♦❢ ❚❛① ❆❞♠✐♥✐str❛t✐♦♥s✳ ❲❤✐t❡✱ ❘✐❝❤❛r❞ ❆✳✱ ❍❛rr✐s♦♥✱ P❛✉❧ ❉✳✱ ✫ ❍❛rr❡❧❧✱ ❆❞r✐❛♥✳ ✶✾✾✸✳ ❚❤❡ ■♠♣❛❝t ♦❢ ■♥❝♦♠❡ ❚❛① ❲✐t❤❤♦❧❞✐♥❣ ♦♥ ❚❛①♣❛②❡r ❈♦♠♣❧✐❛♥❝❡✿ ❋✉rt❤❡r ❊♠♣✐r✐❝❛❧ ❊✈✐❞❡♥❝❡✳ ❏♦✉r♥❛❧ ♦❢ t❤❡ ❆♠❡r✐❝❛♥ ❚❛①❛t✐♦♥ ❆ss♦❝✐❛t✐♦♥❧✱ ▼❛②✱ ✻✸✕✼✽✳ ❨❛❣❛♥✱ ❉❛♥♥②✳ ✷✵✶✺✳ ❈❛♣✐t❛❧ ❚❛① ❘❡❢♦r♠ ❛♥❞ t❤❡ ❘❡❛❧ ❊❝♦♥♦♠②✿ ❚❤❡ ❊✛❡❝ts ♦❢ t❤❡ ✷✵✵✸ ❉✐✈✐❞❡♥❞ ❚❛① ❈✉t✳ ❆♠❡r✐❝❛♥ ❊❝♦♥♦♠✐❝ ❘❡✈✐❡✇✱ ❢♦rt❤❝♦♠✐♥❣✳ ✺✵ ❩✉❝♠❛♥✱ ●❛❜r✐❡❧✳ ✷✵✶✸✳ ♦r ♥❡t ❈r❡❞✐t♦rs❄✯✳ ❚❤❡ ▼✐ss✐♥❣ ❲❡❛❧t❤ ♦❢ ◆❛t✐♦♥s✿ ❆r❡ ❊✉r♦♣❡ ❛♥❞ t❤❡ ❯✳❙✳ ♥❡t ❉❡❜t♦rs ❚❤❡ ◗✉❛rt❡r❧② ❏♦✉r♥❛❧ ♦❢ ❊❝♦♥♦♠✐❝s✱ ✶✷✽✭✸✮✱ ✶✸✷✶✕✶✸✻✹✳ ✺✶